Richarlison's early strike was enough to guide Everton to only their sixth home win of the season as Southampton's alarming slump continued with a 1-0 defeat at Goodison Park
Everton took the lead inside the opening 10 minutes as Richarlison continued his rich recent vein of form in front of goal with his third goal in three games
Southampton left it late to muster any kind of response but could have snatched a point had Moussa Djenepo not blazed wide, or had Jannik Vestergaard managed to bundle the Saints' first attempt on target past Jordan Pickford in the final minute
But Everton held on to secure back-to-back league wins for the first time since Boxing Day as Carlo Ancelotti's side ended a three-game home losing streak to move level on points with Liverpool and to within two points of the top four
For Ralph Hasenhuttl and Southampton, their table-topping early-season form is a distant memory after succumbing to an eighth Premier League defeat in nine which leaves them 14th, seven clear of the relegation zone and looking over their shoulders
Everton came into the game on the high of last Sunday's long-awaited victory at Anfield and having not lost at home to Southampton in the Premier League since 1997, and they needed just nine minutes to take the lead
Gylfi Sigurdsson exploited space vacated by Mohammed Salisu after he came off second best in an aerial duel with Dominic Calvert-Lewin, sliding a pass forward for Richarlison who rounded the on-rushing Fraser Forster before finding the net for the third straight game
Richarlison got his head to a Sigurdsson free-kick on the quarter-hour mark only for Forster to deny him a quick-fire second
 When Everton did manage to beat the Saints goalkeeper, they were denied a second goal by VAR, with Michael Keane's effort ruled out after Mason Holgate headed the ball back across goal from an offside position
Southampton took an age to settle into the game, but the favourable VAR call kicked them into gear, although Everton were in no mood to surrender their lead before the break, with Calvert-Lewin heading a dangerous James Ward-Prowse free-kick away before Pickford was tested
Everton looked to hammer home their superiority early in the second half, but centre-back Ben Godfrey bundled a close-range rebound wide after Ward-Prowse had blocked an effort from Keane, who glanced a header wide moments later having reached a Lucas Digne cross
Southampton had managed to score just one second-half goal in their previous 13 Premier League games and that wretched run continued on a night of frustration on Merseyside
Salisu flashed a near-post header wide before Djenepo blazed their best opening of the game wide with the goal at his mercy with five minutes remaining
It took Southampton until the final minute to register their first attempt on target but when they did, Pickford smothered centre-back Vestergaard's effort to seal Everton's return to winning ways at Goodison
"It's been a very good week, a very good performance
 I really appreciate the teamwork, we were focused defensively, had a good combination in front
 The performance was good, and we deserved to win
"When you are 1-0 up the last minutes are always the same, the opposition team puts a lot of power in and we had to control
 They had practically one opportunity
 Pickford was good in the goal, really secure
 I am really pleased, honestly
"To fight for European places we need to improve the home run, this performance and victory can help us have a better run at home
 It will be a dream to be in the top four at the end of the season
 We are quite close, if we win Thursday, but the season is long - we have to stay in our goal which is to play Europa next season
""Not a good start, first goal, first chance, long ball and we don't defend it well
 We have seen the same goal against Liverpool, it is strange we cannot defend it
 We had a few chances from set-pieces but are in a moment we cannot score
"We had a good second half, the three young lads did what they could
 We did OK in the second half, had a high energy level
 The goals are missing at the moment and without goals it is tough to win games
"We have to work for the luck to come back
 When you don't win games you get under pressure
 To have 30 points shows how much we have done this season
 We are in a tough situation, we know this, but we will fight until the end
""I think Everton may just fall short of the top four, the squad of players is maybe just a bit short
 But if they are to get into the top four, a lot of it will be down to the record of manager Carlo Ancelotti
"Everton's last couple of wins have taken his win percentage to over 50 per cent, and no manager has been close to that since Howard Kendall's first spell
 That is Everton's best-ever manager, so that just shows the job Ancelotti has done since joining the club
"With Ancelotti in charge, anything is possible in terms of the top four
"In a game where both sides managed just a solitary shot on target each, Everton's quality in the decisive moments proved crucial
Richarlison was razor sharp to convert his early chance but Pickford's contribution to deny Vestergaard, despite having spent the previous 90 minutes as a bystander, ensured Everton came away with all three points
Having endured difficult spells this season, back-to-back clean sheets for the first time this campaign offered a timely reminder that Pickford is getting back to his best
Carragher told "Pickford wins Everton two points with that late save
 When you also think about his performance last week at Anfield
 Everton did brilliantly to get their head on so many set-pieces
 Vestergaard was slipping but it was a big moment for Pickford
"He's a player who had the finger pointed at him, but he's been in great form the past two games, hence why Everton have kept clean sheets
"Everton travel to face West Brom on Thursday, live on ; kick-off is at 6pm
Southampton visit Sheffield United on Saturday, also live on ; kick-off is at 3pm
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