Steven Gerrard and Juan Mata scored pivotal goals as Liverpool and Manchester United each posted victories over obdurate opposition in the Premier League on Tuesday.

Liverpool captain Gerrard, the subject of speculation about his Anfield future this week, stroked home the crucial second goal as his side came from behind to win 3-1 at 10-man Leicester City.

Victory lifted Brendan Rodgers's side up to eighth place, but they remain five points off the Champions League berths after Mata's fortuitous strike earned fourth-place United a 2-1 success at home to Stoke City.

The Spaniard saw a free-kick from wide on the right drift straight into the net in the 59th minute at Old Trafford, sending United to within a point of third-place Southampton, who visit Arsenal on Wednesday.

Leaders Chelsea entertain Tottenham Hotspur on Wednesday, while second-place Manchester City travel to Sunderland.

Explaining his decision to rest 34-year-old Gerrard for Liverpool's 1-0 win over Stoke at the weekend, Liverpool manager Rodgers told BT Sport: "Steven Gerrard was rested last weekend with tonight in mind.

"When you rest a player, people ask why. When you play them, you are asked why aren't you resting them. The energy from being rested at the weekend gave him the energy to play tonight."

Despite Gerrard's return to the starting XI, Liverpool made a wobbly start at the King Power Stadium.

Esteban Cambiasso should have put Leicester ahead in the 20th minute when under-fire Liverpool goalkeeper Simon Mignolet played the ball straight to him, only for the Argentine midfielder to roll the ball wide.

But Leicester went ahead two minutes later, with Leonardo Ulloa's shot hitting the post and cannoning into the net off Mignolet's back for an own goal after Martin Skrtel had blocked on the line from Jamie Vardy.

The hosts' lead lasted just four minutes, however, with Adam Lallana drilling home an equaliser from Rickie Lambert's knock-down.

Gerrard's moment arrived nine minutes into the second period. Wes Morgan could only get a toe to Raheem Sterling's left-wing cross and Gerrard strode forwards to steer the loose ball into the bottom-right corner.

Gerrard keeps mum

After Morgan was sent off in the 63rd minute for hauling back Lambert, Sterling's back-heel teed up Jordan Henderson to sweep home a late third for Liverpool following a fumble by home goalkeeper Kasper Schmeichel.

Rodgers revealed before the game that Gerrard has been offered a new contract, but when asked if he was ready to commit to a new deal, the former England captain said: "I will decide when I am ready.

"There is nothing to say. When there is, the fans know I will come out and say it."

A knee injury to Wayne Rooney saw 19-year-old James Wilson handed a surprise start for Manchester United, who took a 21st-minute lead when Marouane Fellaini headed in Ander Herrera's inviting left-wing cross.

Steven Nzonzi equalised for Stoke six minutes before half-time, lashing home from outside the box after a dart by Bojan Krkic.

But Mata's goal gave United a fourth straight victory, with Marcos Rojo's leap distracting visiting goalkeeper Asmir Begovic and allowing the former Chelsea playmaker's free-kick to nestle inside the left-hand post.

After seeing his goalkeeper David de Gea pull off a pair of stunning late saves, United coach Louis van Gaal said: "The last few moments were not necessary, but it is always like that.

"We have struggled until the end in the Premier League. It is common. I'm happy with the result. Tomorrow (Wednesday) we have a Christmas party and it's important we can enjoy that."

West Ham United remain a point behind Van Gaal's side in fifth place after coming from behind to win 2-1 at West Bromwich Albion.

Craig Dawson's 10th-minute header put the home team in front, but Kevin Nolan equalised 15 minutes later and James Tomkins gave West Ham victory with a header in first-half injury time.

Swansea City climbed to sixth place, two points behind West Ham United, after well-taken late goals from Ki Sung-yueng and Wayne Routledge secured a 2-0 success at home to second-bottom Queens Park Rangers.

Burnley climbed out of the relegation zone following a 1-1 draw at home to Newcastle United, with Papiss Cisse earning the away team a point after George Boyd had put the hosts ahead with a strike from distance.

Meanwhile, Christian Benteke scored the only goal as Aston Villa moved five points clear of the bottom three with a 1-0 success at Crystal Palace.