Iliman Ndiaye's first-half penalty secured back-to-back wins for Everton, who edged out Brighton & Hove Albion 1-0.
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Ndiaye scored for the second match running as the Toffees claimed all three points in what was David Moyes' 700th Premier League match in charge.
The Senegalese netted from the spot just before half-time after Joel Veltman was pulled up for handball by the referee following a VAR review.
Brighton controlled large periods of the second half as they pushed for an equaliser, but the visitors held out to record successive league victories for the first time since April.
Moyes' side remain 16th but move seven points clear of 18th-placed Ipswich Town, while Brighton stay ninth after missing the chance to close the gap on the top four.
How the match unfolded
Everton suffered an early blow with a hamstring injury forcing Dominic Calvert-Lewin off after just 13 minutes.
Nevertheless, the visitors took the lead three minutes before the break. Referee Tim Robinson gave a penalty following a VAR review, ruling Veltman had handled in the box, and Ndiaye converted from the spot.
Brighton sought a response after the break. Kaoru Mitoma – looking to become the first Japanese player to score in three successive Premier League matches – curled an attempt wide, while substitute Georginio Rutter was also narrowly off target from distance.
Beto shot wide at the other end with what was Everton’s only effort of the second half. But despite that – and enjoying just 15 per cent of possession after the break – they held on for another crucial three points to drag them further away from trouble.
Seagulls' Amex winless run goes on
Following a difficult recent spell of form, Brighton appeared to have turned a corner, having gone seven matches without defeat in all competitions.
Today’s match, therefore, presented them with a decent opportunity to continue climbing the table and close the gap on the top four.
However, Fabian Hurzeler’s side were on the back of a four-match winless streak on home soil in the Premier League.
Despite looking the brighter of the two sides during the first half, they failed to register a single shot on target, while Veltman’s handball was punished by Ndiaye tucking away the penalty.
Their attacking threat undoubtedly improved after the break. Nevertheless, from the 12 attempts they recorded, Jordan Pickford was only forced to save one of them.
As Everton kept things tight, making a series of impressive blocks to keep them at bay, the Seagulls saw their winless streak continue at the Amex Stadium.
Things do not get any easier for Hurzeler’s side as next weekend sees them travel to third-place Nottingham Forest, albeit Nuno Espirito Santo’s side will be reeling from their 5-0 defeat by AFC Bournemouth on Saturday.
Tenacious Toffees march on
The omens did not appear overly positive for Everton, who had won just one of their last 21 Premier League away matches, while only scoring once in their six most recent outings.
Nevertheless, the Toffees had cause for optimism, having been victorious in two of their last three visits to the Amex Stadium.
They were also fresh from a morale-boosting 3-2 victory over Tottenham Hotspur the previous weekend, giving Moyes the first win of his second spell in charge.
Ndiaye, who scored a fine individual goal against Spurs, was on target again, calmly slotting home what proved to be the winner from the penalty spot.
On the backfoot for large periods of the second half, the Toffees were forced to dig really deep. They did, though, and Moyes punched the air in delight upon hearing the final whistle, giving him the perfect present on the day he joined Arsene Wenger and Sir Alex Ferguson in the 700 club.
Everton will be confident of building on their recent momentum when they welcome struggling Leicester City to Goodison Park next weekend.
Club reports
Brighton report | Everton report
What the managers said
Fabian Hurzeler: "We played against a very disciplined team. We weren't clean enough in the first half and didn't force it enough. We did not have good box positioning and then we faced an opponent who tried to break the rhythm all the time. Then it's very difficult."
David Moyes: "My heart has still not settled after that! It ended up a great results for us. Really important for us, we are too close to the bottom. A lot of belief coming back. Brighton put us to the sword, but we got the goal that mattered."
Next PL fixtures
Key facts
Moyes picked up just his second Premier League win against Brighton, having won just one of his first 10 league matches against the Seagulls (D5 L4), all as West Ham United manager.
Everton have won back-to-back Premier League matches for the first time this season and for the first time under Moyes since a run of three in March 2013 (v Reading, Manchester City and Stoke City).
Brighton have lost for the first time in seven Premier League matches (W2 D4 before today), bringing to an and what was their longest unbeaten run in a single season since December 2021-February 2022 (a run of 7).
Moyes took charge of his 700th match in the Premier League (430 Everton, 34 Manchester United, 38 Sunderland, 198 West Ham), becoming the third manager to reach that figure in the competition, after Arsene Wenger (828) and Alex Ferguson (810).