Ndiaye scored for the second match running as the Toffees claimed all three points to highlight a landmark day for Moyes, who is on his second spell with the club. 

The Senegalese netted from 12 yards just before half-time after Joel Veltman was pulled up for handball by the referee after a video assistant refere (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 remains 16th on the table but moved seven points clear of 18th-placed Ipswich Town, which was beaten 4-1 by leader Liverpool at Anfield.

Brighton stays ninth after missing the chance to close the gap on the top four, from which it is now seven points adrift.

Moyes oversaw only his second Premier League win over Brighton in 11 attempts – drawing five and losing four.

It was an ideal way to mark his 700th match in charge in the division, making him the third manager to reach that milestone after Arsene Wenger (828) and Alex Ferguson (810).

"My heart has still not settled after that," Moyes said after the match.

"It ended up a great result 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."

Defender James Tarkowski backed up what Moyes said, admitting that his nerves were so bad that he couldn't even watch Ndiaye's penalty.

"I was nervous [for the penalty]. I didn't even watch. I don't know how it went in but I don't care," he said.

"Calm and collected, that is what we expect of him [Ndiaye]. We've not scored loads, we got a few last week, so it is nice to get one whichever way it comes.

"We got the goal, defended well and we knew that the second half was going to be tough. We have seen them come back against Man City and other teams here which shows how good they are.

"We have been resilient, grinded it out with ten men for 10-15 minutes or so, and everyone from the front of the pitch to the back played their part. Very proud of the lads. Let's move on and go again.

"We did deal with it [Brighton's threat] and it hasn't always been that way this year. We have given leads away and gifted teams goals at times but today was a real team performance. The fans can enjoy their trip home because it has been tough at times, they can enjoy that one."

Brighton head coach Fabian Hurzeler, meanwhile, was critical of his own team's inability to break the opposition down and the referee.

"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," he said.

"When the referee says that he won't send a player off for time-wasting that says it all really. I don't understand. When the rules are like this then you could send someone off. The referees should use it.

"We are honest with each other, self-critical and that is why we have to keep working. Next game we will analyse what went wrong, what we have to improve and keep going."