In the 85th minute, Adam Armstrong scored a crucial goal to lift the Saints off the bottom of the table. Just moments earlier, Everton substitute Beto had a close call as he headed the ball against the crossbar from inside the six-yard box.
A drab first half gave way to an improved second with Southampton goalkeeper Aaron Ramsdale pushing Orel Mangala's shot over the crossbar. However, his best save came in the 67th minute when he superbly tipped Michael Keane's goal-bound header onto the right post.
The hosts rode their luck as Jan Bednarek escaped with only a yellow card following a VAR check for bringing down Beto as he tried to burst through.
Jack Harrison then poked wide before Beto improbably missed from close range, leading to Southampton breaking up the other end and taking the lead through Armstrong's clinical finish.
TrendingSean Dyche's side then thought they had equalised in the 89th minute when Beto brilliantly controlled a long ball forward and slotted past Ramsdale, but VAR came to Southampton's rescue by ruling the goal out for offside and ending Everton's five-game unbeaten run.
Everton manager Sean Dyche said:
"Our shape was good, our play was good, we made enough chances away from home to win the game. The big calls didn't go for us either, particularly the one where Beto goes straight through. How that's not a sending-off, I don't know. He's inside the V as the referees work on.
"I know their defender, I don't think he's that quick to get around him from there but we don't get those big decisions often.
"It's not only a sloppy goal, we should have scored at the other end. They get a breakaway, sometimes that happens from a misshapen team. We had plenty of desire to get back and they got that out of nothing at that stage of the game."
Southampton manager Russell Martin said:
"It's huge for us as a team, as a group, as a club, and the clean sheet as well. We played some beautiful football, some brilliant football and had to dig in at times. Rambo (Aaron Ramsdale) made a couple of brilliant saves.
"We scored a goal, which comes from their attacking set play and amazing composure in our box. It starts there with the guys not just clearing the ball and staying so brave. I'm really proud of them for that. It's a really good goal.
"I'm really grateful to the boys for sticking through some tough moments today as well as sticking with what we want to be and who we want to be.
On Beto's disallowed equaliser: "The angle we had on the iPad in the dugout it looked so tight. We were probably pessimistic at that point. I'm glad it's gone for us. I guess that's what VAR was there for and the players deserved it."