James Ward-Prowse's second goal in as many Premier League matches and a bizarre Lucas Digne own goal lifted Ralph Hasenhuttl's men three points clear of the drop zone.
The Saints, 2-1 winners at Leicester City last weekend, were on top from start to finish at St Mary's in a confident response to their midweek FA Cup exit to Derby County.
The fit-again Danny Ings was a menace throughout the first half and Everton – which grabbed a late consolation through Gylfi Sigurdsson – never came to grips with the home side's intensity, slumping to its fifth league loss in seven.
Ings returned to Southampton's starting XI after two matches out with a hamstring injury and twice tested Jordan Pickford during the opening half hour.
The goalkeeper first reacted well to scoop away a glancing header and next parried the on-loan Liverpool man's first-time drive after Jan Bednarek's ball over the top.
There was time left in the first half for Ings to threaten once more, his determined dribble ending with Andre Gomes inadvertently poking the ball into the base of his own upright.
The breakthrough came from a less likely source five minutes after the interval as Ward-Prowse collected the ball in midfield, drove towards the edge of the area and unleashed a superb strike that flew past Pickford.
Southampton was buoyed and put the result beyond Everton's reach in unusual fashion, left-back Digne's attempt to nick the ball away from Nathan Redmond resulting only in the ball squirting into the bottom corner from 25 yards.
Sigurdsson did halve the deficit with a calm side-footed finish from the edge of the area in the 91st minute, but the visitor left it too late to snatch an unlikely equaliser.