A second half strike by substitute Jakub Blaszczykowski booked Poland's ticket into the last-16 at Euro 2016 and sent Ukraine home without a point.
The Group C win in Marseille propelled Poland further than they have ever gone in a European Championship and they will meet Switzerland in the last-16.
"For the first time in Polish history we have qualified from the Euros group stage, the first time in three attempts," coach Adam Nawalka said.
The 30-year-old Blaszczykowski was put on the substitutes' bench, but his left-footed curler seven minutes after his second-half introduction decided the tie.
"Blaszczykowski has a great influence on the way we play, he showed that tonight once he came off the bench, he increased the quality of our play," said Nawalka.
"I count on him in the coming game, certainly he will start from the first minute," he added.
With two 1-0 wins against Northern Ireland and the Ukrainians either side of a scoreless draw against Germany, Poland finished in second place in Group C on goal difference.
After defeats to Germany and the Irish, Ukraine were already eliminated before the game in the Stade Velodrome. They have become the first team to go five matches without a goal in Euro history.
With pride at stake for Mykhailo Fomenko's men though and a chance of topping the Group C table beckoning for Poland, both teams attacked from the off.
Poland's formidable strike pair Arkadiusz Milik and Robert Lewandowski each had early chances, the Bayern Munich star volleying the more clearcut of the two over Andriy Yatov's crossbar.
Ukraine's Andriy Yarmolenko should have scored on the quarter hour but chipped wide when one—on-one against Lukasz Fabianski.
- Sub strikes -
Lewandowski found more room than in the previous two games and had a drive deflected wide on 20 minutes, but from the half-hour Ukraine began to assert themselves.
With impressive teenager Olexandr Zinchenko, 19, orchestrating from midfield, Ukraine began to stretch Poland on occasion.
Winger Yevhen Konoplyanka drilled a low effort narrowly wide on the half hour. Soon after left-back Bohdan Butko crossed when a shot seemed a better option.
But with lone striker Roman Zozulya proving ineffective, Ukraine could not find their first goal since their opening game at the Euro 2012 tournament that they co-hosted with Poland.
Instead, it was Poland's sub Blaszczykowski, one of four switches by Nawalka, who broke the deadlock with a delightful strike.
Fed by Milik with a reverse pass on the right of the area in the 53rd minute, he worked the ball onto his left foot and curled a shot inside the far-post to send the Velodrome, decked out mainly in Poland's red and white, into raucous celebration.
A minute later, with the fans still jumping, Poland's own 19-year-old Bartosz Kapusztka nearly made it two but fired wide of both Pyatov and the post.
The Poles eased up after that, a Milik header well wide with 15 minutes to go the nearest they came to making it two.
In truth Mykhailo Fomenko's men rarely troubled Fabianski.
Although captain Ruslan Rotan, later awarded man-of-the-match, forced him to dive eight minutes from the end and Zozulya headed narrowly wide soon after, two second-half blasts over the bar from Konoplyanka and Zinchenko were more typical of Ukraine's miserable tournament.
“It was a difficult match today it was maybe even more difficult than against Germany," Fabianski said.
"We didn't have as much possession as we wished, but despite the fact that we didn't play particularly well we won," he added.
Ratan blamed Ukraine's mentality for his side's forlorn Euro 2016 experience.
"We have to work on the psychological level of the team not the sporting level," he said.
"We have very good young players so in the future we will see a stronger Ukraine," he added.
"I don't have any complaints about the players," Fomenko said.
"My only wish would be that the experience that they have acquired here will be used later, that if they work hard on the pitch they will also be able to use their chances in front of goal".
AFP
Wed Jun 22 2016
Poland's midfielder Jakub Blaszczykowski (R) celebrates after scoring during the Euro 2016 group C football match between Ukraine and Poland at the Velodrome stadium in Marseille on June 21, 2016. - AFP PHOTO / ANNE-CHRISTINE POUJOULAT
Who is Prabowo Subianto, incoming president of Indonesia?
A wealthy ex-general with ties to Indonesia's popular outgoing president and its dictatorial past, looks set to be its next leader.
Iran's supreme leader says Hamas leader's death will not halt 'Axis of Resistance'
The "Axis of Resistance", built up with years of Iranian support, includes Hamas, the Lebanese Hezbollah group, the Houthi movement in Yemen, and various Shi'ite groups in Iraq and Syria.
Putin says Russia willing to seek compromises between Iran and Israel
Russia is ready to help seek compromises between arch-foes Israel and Iran, President Vladimir Putin said on Friday, saying these would be difficult but possible.
What proposals will Russia push at the BRICS summit?
The proposal is also to establish a BRICS reinsurance company to allow uninterrupted shipment of goods and key commodities between members.
Indonesia's free meals plan in the spotlight as Prabowo readies for office
Prabowo calls the programme one of the main drivers of economic growth, eventually set to add an estimated 2.5 million jobs.
Astro AWANI's revamped English news website, AWANI International, launches on Oct 21
Astro AWANI's revamped English platform delivers in-depth global news and expert analysis to keep you informed on key developments.
Israeli strikes kill 33 people in Jabalia refugee camp in Gaza, medics say
Residents of Jabalia said Israeli tanks had reached the heart of the camp after pushing through suburbs and residential districts.
Liam Payne's ex-partner calls for media restraint after 'painful' death
Cheryl Tweedy used her statement to urge the media to remember they had a seven-year-old son, Bear, who could read the reports.
Analysts: Indonesia's strong MoF leadership team to boost investor confidence
Sri Mulyani Indrawati as head of Indonesia's Ministry of Finance is expected to instil confidence among investors.
Biden offers both a carrot and a stick to Israel as his term nears an end
Israel has frequently resisted US advice and has caused political difficulties for the Biden administration.
Putin says BRICS will generate most of global economic growth
Russian President Vladimir Putin will host a summit of the group in the city of Kazan on Oct. 22-24.
ISIS Malaysia's perspective of Budget 2025
An excellent rakyat-centric budget under the overarching principle of a caring and humane economy.
Budget 2025: Record increase in STR, SARA aid initiatives
The government will provide a significant boost to the Sumbangan Tunai Rahmah (STR) and Sumbangan Asas Rahmah (SARA) initiatives next year.
Budget 2025: EPF contributions to be made mandatory for foreign workers – PM Anwar
The government plans to make it compulsory for all non-citizen workers to contribute to the Employees Provident Fund (EPF).
What policies to expect from Indonesia's new President Prabowo
Prabowo will be open to foreign investment, his aide has said, such as by offering investors management of airports and sea ports.
Budget 2025: Govt allocates RM470 mil to empower women's participation in PMKS
The Women's Leadership Apprenticeship Program will be intensified as an effort to produce more female corporate personalities.
Israel sends more troops into north Gaza, deepens raid
Residents of Jabalia in northern Gaza said Israeli tanks had reached the heart of the camp, using heavy air and ground fire.
Indonesia ramps up security ahead of Prabowo's inauguration
Prabowo Subianto will be sworn in as Indonesia's president on Sunday with Vice President-elect, Gibran Rakabuming Raka, also taking office.
Immediate allocation of RM150 mil for local authorities, DID to tackle flash floods
Datuk Seri Anwar Ibrahim said this allocation is intended to address the recent flash floods that hit the capital and several major towns.
Budget 2025: Sabah, Sarawak to continue receiving among highest allocations - PM
Sabah and Sarawak continues to be prioritised under Budget 2025, with allocations of RM6.7 billion and RM5.9 billion respectively.