Swansea after a series of 6 matches, during which he scored just 1 point, in the last two rounds defeated Stoke City 2-0 and played a 1: 1 draw with Manchester United.
29' - GOAL! Swansea 1-0 Everton (Llorente).
Everton have not sustained any new injuries but Morgan Schneiderlin was in contention to return, however his thigh injury will keep him on the sidelines, with Ronald Koeman setting next Friday's home game against Watford as the return date for the French midfielder.
This is Swansea's first ever home league win against Everton.
For Saturday opponents Swansea, striker Fernando Llorente has recovered from a stomach bug and is fit to lead the Swans attack as they vie for Premier League survival. Following closely behind, is midfield general Gylfi Sigurdsson, who has found the net on nine occasions domestically, reaching ten in all competitions.
"It's one of my proudest moments", said Clement, a former assistant at Real Madrid, Bayern Munich, Paris Saint-Germain, and Chelsea who is starting to look the part as a coach in his own right.
Jefferson Montero (hamstring) is unlikely to play again this season.
Swansea boss Paul Clement hopes to avoid a historic Premier League relegation play-off with Hull. The Toffee's are now ranked 6th in the league, and the club has big aspirations of European football next season.More news: Man Utd defender Luke Shaw to miss rest of season
City climbed above Liverpool into third place on goal difference, and opened up a four-point gap to fifth-place Manchester United, which plays at Arsenal on Sunday. Clement views Saturday's home game against seventh-placed Everton as the biggest remaining obstacle between his team and safety.
But it was Everton who created the first opening inside 45 seconds as Romelu Lukaku headed straight at Lukasz Fabianski.
The young centre back was certainly a contender for Man of the Match and both stand-out players were on-par in an excellent performance.
Will either Hull or Swansea be able to change the picture at the bottom?
The Toffees piled bodies forward in search of a dramatic equaliser but some terrific defending, inspired by Alfie Mawson, meant the home side hung on for three precious points.
Now is the flawless time for the recent stalemate to end and for one side to truly stake a claim for survival.
While it appears to be a straight two-horse race between Hull and Swansea, there are still several clubs whose Premier League status is not yet entirely secure.