Manchester City boosted their hopes of qualifying for the UEFA Champions League next season as they scored two late goals to secure a 2-0 win over Everton.

City had to wait until the 84th minute to break the deadlock on their final trip to Goodison Park, where Nico O’Reilly put them in front with a close-range finish after Everton’s defence had largely frustrated Pep Guardiola’s side.

But once one goal arrived, another followed – substitute Mateo Kovacic sealing the points with an excellent finish on the slide.

Everton had earlier hit a post through James Tarkowski, who subsequently went off injured, while Jarrad Branthwaite saw a close-range header saved by Stefan Ortega.

City move into fourth place, a point behind Newcastle United in third, while Everton remain 13th, having lost a Premier League game at home for the first time since January.

How the match unfolded

Chances were few and far between in a cagey first half. Matheus Nunes hit a low drive on target, though it was dealt with by Jordan Pickford, before Tarkowski’s glancing header from James Garner’s corner struck the right-hand post.

That Everton opportunity sparked City into life – Kevin De Bruyne’s curling left-footed attempt seemed destined for the bottom-left corner until Jake O’Brien stooped low to head it wide.

Ortega reacted well to keep out Branthwaite’s looping header after the restart, while Abdoulaye Doucoure saw an effort bravely blocked by Josko Gvardiol, though an apparent hamstring injury to defensive stalwart Tarkowski knocked Everton’s rhythm.

An error from replacement Michael Keane gifted Omar Marmoush a chance the Egyptian failed to take, but O’Reilly made no mistake when he got in front of the Everton centre-back moments later to tap in from Nunes’ centre.

Kovacic then directed a fine finish into the left-hand corner to seal a potentially crucial win in City’s push for the top five.

City stutter but late surge seals it

City pulled off a remarkable comeback in their last outing, overturning a 2-0 deficit to defeat Crystal Palace 5-2, with De Bruyne playing a starring role, but this was a much different type of win.

De Bruyne began the game in his typical attacking midfield role, but moved with freedom throughout, even playing as a false nine in certain passages across the first half, with Marmoush drifting to the left to double up with Savinho. City’s captain was their most dangerous player, though, fluid in his movement and sharp in his passing,

But despite controlling the possession, as they do so well, City struggled to puncture a resolute Everton backline, and they had to rely on first the woodwork, and then Ortega, to keep the scores level.

The midfield trio of Ilkay Gundogan, Bernardo Silva and Nico Gonzalez looked slightly off the pace, leaving De Bruyne isolated and overburdened in central midfield.

It was youngster O’Reilly – one of the bright sparks from their frustrating season – that was ultimately in the right place at the right time to nudge City ahead. Substitute Kovacic made absolutely sure with, like O’Reilly, his second goal in as many matches.

Next up for City is a home encounter with Aston Villa, in a huge meeting in the race for Champions League spots.

Toffees come unstuck at Goodison

There are now just two games left for Everton at Goodison Park, with strugglers Ipswich Town and Southampton visiting in May.

David Moyes’ team gave a good account of themselves, but he will have probably been disappointed they did not offer more of an attacking threat, despite showing some positive signs with those big chances for Tarkowski and Branthwaite.

Doucoure was Everton’s hero last time out, snatching three vital points with a stoppage-time winner in an evenly-matched contest against Nottingham Forest, but he could not make a telling impact, while Iliman Ndiaye cut a frustrated figure out on the left, and Jack Harrison flitted in and out of things, although he did get close to a perfectly-weighted cross from Vitalii Mykolenko at one point.

Moyes may well point to that injury to Tarkowski as the turning point. An ever-present since he joined Everton from Burnley, the centre-back left a void in defence when he trudged off, and Keane was at least partially at fault for City’s opener.

Everton round off April with a trip to London to face Chelsea, before they are back at home for that visit of Ipswich – Moyes will not want Goodison Park to witness another Toffees defeat.

Match reports

Everton report | Man City report

What the managers said

David Moyes: "We might have just ran a little bit out of juice in the second half. Losing James Tarkowski was a blow to us. We played really well for 60 minutes and then just ran out of it a little bit in the final 30 minutes.

"They have quality and more to bring off the bench. We'd done a good job of nullifying them. I was disappointed with the goal we conceded. We gave away a sloppy pass and then didn't defend the box well enough."

Pep Guardiola: "It was massively important. We have three games at home and two away. Our qualification will be at home, but they are tough games. Stefan Ortega saved the balls that he needed too and the players made a step up in the second half.

"We were more incisive. I'm really pleased with the game we played in the second half. The players performed really well, all of them."

Match officials

Referee: Simon Hooper. Assistants: Adrian Holmes, Simon Long. Fourth official: Bobby Madley. VAR: Darren England. Assistant VAR: Scott Ledger.