Danny Ings scored his 19th goal of the season but Southampton could not make their early dominance count in a 1-1 draw with Everton.
Saints were in the ascendancy from the first whistle and James Ward-Prowse missed a golden opportunity from the penalty spot after he was fouled by Andre Gomes.
Ings, who had already hit the bar, found the net (31) when latching onto a Stuart Armstrong scuffed shot. Everton looked short on ideas but Richarlison scored (44) against the run of play just before the break.
Carlo Ancelotti switched Everton's tactics in the second period which helped contain the sprightly visitors as the game fizzled out to an underwhelming conclusion.
Everton: Pickford (6), Coleman (7), Keane (6), Mina (6), Digne (7), Davies (6), Gomes (5), Iwobi (5), Gordon (6), Richarlison (7), Calvert-Lewin (6)
Subs used: Sidibe (7), Sigurdsson (6), Kean (6)
Southampton: McCarthy (7), Walker-Peters (7), Bertrand (7), Bednarek (6), Stephens (6), Romeu (6), Ward-Prowse (8), Armstrong (6), Redmond (7), Adams (6), Ings (8)
Subs used: Long (6), Hojberg (7)
Man of the match: Danny Ings
With four games to go in the season, Everton are 11th on 45 points while Saints are a point behind them.
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How the spoils were shared…
Everton had some questions to answer after their lacklustre performance against Tottenham but it was the visitors who played with all the intensity and dominated possession, following on from their win over Manchester City.
The game could have been over considering how many chances Southampton created in the opening period.
Armstrong had a goal chalked off for a marginal offside after turning home a Che Adams volley before the brilliant Ward-Prowse had a goal-bound effort blocked by Adams.
- Everton made two changes from the defeat at Spurs with Yerry Mina and Anthony Gordon coming in.
- Southampton were unchanged from the win over Manchester City. Pierre-Emile Hojbjerg, who is reportedly wanted by Everton, was back on the bench.
The movement from Ings was a constant problem for the Toffees and he was denied by a combination of Jordan Pickford and the crossbar following a pin-point Ward-Prowse corner.
Gomes summed up Everton's sloppy approach when lazily challenging Ward-Prowse in the area and referee Lee Mason was on the spot to award the penalty. However, Ward-Prowse smacked the spot-kick off the crossbar.
Usually a missed penalty would bring a momentum shift in the game but Southampton carried on pressing and carried on forcing Everton to defend. The goal came minutes later.
Armstrong's scuffed shot fell perfectly into Ings' path and he shifted his body quickly to take the ball around Pickford before poking home a deserving opening goal that takes him to within three goals of Jamie Vardy in the Golden Boot race.
The response from Everton wasn't instantly forthcoming but one moment of quality got them level before the break.
Lucas Digne picked out Richarlison with a fantastic 50-yard ball that split the two Southampton centre-backs and the Brazilian supplied the finish after an excellent first touch to set up the chance.
Ancelotti's decision to replace right-sided midfielder Alex Iwobi with defender Djibril Sidibe at half-time had the desired effect as with Seamus Coleman at times tucking in as a third centre-back helped stop Ings finding so much space to work in.
Chances were in short supply in an evenly contested second period.
Dominic Calvert-Lewin, who has not scored in nine matches and was quiet again, fluffed his one chance when he failed to connect properly with Tom Davies' diagonal pass and Richarlison felt he was denied a goalscoring opportunity by Jan Bednarek but referee Mason decided the foul warranted only a yellow card and VAR agreed.
Man of the match: Danny Ings
The song was spot on. Ings is only getting better.
His game is fast becoming very similar to that of Vardy, who is he chasing in the Golden Boot race. Like Vardy, perhaps he should start taking the penalties.
Constantly on the move, Ings gave Michael Keane and Yerry Mina so many problems, especially in the first half, with his clever movement down the channels. He never switches off as shown by his quick reactions and finish for the opening goal.
Ings has now scored 44 per cent of Southampton's league goals this season (19/43); this is the largest share of team goals for any player at any side in the competition this campaign. He's absolutely vital for what Ralph Hasenhuttl is trying to build.
What the managers said...
Everton boss Ancelotti said: "The performance was not good in the first half, much better the second half and we were more in control.
"The key point for the first half was we left too much space between lines and they were controlling possession.
"Second half was much better, we started to win more second balls, more fighting.
"It was a fantastic goal (from Richarlison), a fantastic finish but we were lucky in the first half, we didn't deserve to be drawing.
"It was a difficult game, Southampton played better than us but I think the result was quite fair."
Southampton boss Hasenhuttl: "I think we can kill the game in the first half with a little bit more clinical finishing. The post, penalty and everything.
"The last game we have given 26 chances or shots away. This time today I think it was two or three and you concede a goal.
"But I think we didn't play like an away team. I think we played also in possession quite a grown-up game and this is for me a good thing."
- Southampton have earned 27 points away from home this season, the fourth-most of any Premier League side after Liverpool (41), Chelsea (30) and Manchester City (28).
- Everton forward Richarlison scored his 30th Premier League goal. He is the fifth Brazilian to reach this figure after Roberto Firmino (56), Philippe Coutinho (41), Gabriel Jesus (38) and Willian (37).
- Ings has scored in five separate Premier League games against Everton but has never beaten them - only Alan Shearer v Liverpool (7) and Teddy Sheringham v Chelsea (6) have scored in more games against an opponent without finishing on the winning side.
Everton have a trip to Wolves next up on Sunday, live on Sky Sports. Meanwhile, Saints are back in action on Monday with a trip to red hot Manchester United, also live on Sky Sports.