Manchester United defender Harry Maguire chases the ball during the Premier League match against Chelsea on Monday in London. Photo: VCG

Headed goals from Anthony Martial and captain Harry Maguire earned Manchester United a hard-fought 2-0 win at toothless Chelsea on Monday amid more VAR controversy, putting them back in the hunt for a top-four Premier League finish.

The VAR system made the headlines once again after two Chelsea efforts were ruled out and England international Maguire escaped sanction for a kick out at Michy Batshuayi.

In a high-tempo, if often scrappy, game Ole Gunnar Solskjaer's United side made the most of their chances while Chelsea, whose form at home has been suspect all season, squandered a string of opportunities.

Defeat left Chelsea fourth, a point clear of resurgent rivals Tottenham Hotspur led by their ex-coach Jose Mourinho. Chelsea host Spurs on Saturday. United, another of Mourinho's old clubs, rose to seventh, three points behind Chelsea.

"It was a solid performance," said Maguire. "We knew we had to get the win to close the gap. It's a big three points."

Chelsea captain Cesar Azpilicueta added, "In two key moments we lost the game. We created clear chances and were looking good but we were punished before halftime."

A fine glancing header from Martial just before halftime from an Aaron Wan-Bissaka cross put the visitors ahead. It was United's first Premier League goal in four games.

Defender Maguire made it two in the 66th minute, losing marker Antonio Rudiger to head home from a corner by United's new Portuguese signing Bruno Fernandes.

Chelsea may feel hard done by ­after Maguire appeared to kick Batshuayi in the groin after he fell toward him on the sidelines after the pair challenged for the ball in the first half.

"I know I caught him and I felt he was going to fall on me and my natural reaction was to straighten my leg to stop him," Maguire said. 

"It wasn't a kick out and there was no intent."

In the second half Chelsea netted twice only to be left disappointed. Kurt Zouma thought he had scored from a corner in the 54th minute but VAR ruled that there was a push in the area by Azpilicueta on United's Brandon Williams.

Then substitute Olivier Giroud's header in the 77th was canceled out when VAR showed the toe of his boot was offside.

"You want the right decisions to be made and we're happy they were made, because they weren't being made without that help," said United manager Ole Gunnar Solskjaer.

"[Giroud's effort], that's offside. [Zouma's] I just looked at the screen and it looks like a push in the back. So, for me, that's not a goal."