Seamus Coleman gave the hosts the lead with a marvellous individual effort, but Gaston Ramirez equalised from fully 35 yards with a dipping strike that deceived stand-in goalkeeper Joel Robles.
However, Chelsea loanee Lukaku was on hand to finish a terrific sweeping move just three minutes later and keep Everton in the hunt for European places.
Were it not for Thursday's loss to Sunderland, Everton would have been celebrating an unbeaten year at home, but they responded to that set-back with a measured performance in front of their fans.
Leighton Baines returned to Roberto Martinez’s XI and Robles made his first Premier League start for Everton in place of the suspended Tim Howard, with Kelvin Davis returning to the Southampton goal ahead of Paulo Gazzaniga and being called into action by Ross Barkley from Coleman’s cross in the third minute.
The hosts’ bright start paid off six minutes later when right-back Coleman picked the ball up on his flank and burst into the area before smashing an unstoppable strike into the top corner.
It was the Irishman's fifth goal of the season, already surpassing his tally for the previous four campaigns combined.
Southampton began to find their feet as the game wore on, and several had chances in a matter of seconds after 65 minutes, Luke Shaw having a low drive blocked, before Jay Rodriguez's effort was deflected wide.
