Lukaku struck the winner with his ninth goal of the season, and his first in six matches, as Everton continued their assault on the Champions League places.
Roberto Martinez's side reach the halfway stage of the season with 37 points, having lost just two of their first 19 games.
They were made to work hard by Mauricio Pochettino's Southampton, whose heads did not drop after Coleman cut inside James Ward-Prowse and slammed the ball into the top-left corner for his third goal in five games.
They got a deserved equaliser when substitute Gaston Ramirez saw his dipping long-shot evade the grasp of goalkeeper Joel Robles.
But parity lasted only three minutes, until Lukaku's powerful left-foot shot finished off a slick move involving Steven Pienaar and James McCarthy.
9' - GOAL: Everton 1-0 Southampton - Coleman cuts in from the right, leaving Ward-Prowse for dead before beating Kelvin Davis with a powerful shot into the far top corner.
37' - EVERTON CHANCE - Lukaku attempts to square the ball to the unmarked Bryan Oviedo, but the ball is cut out by a vital intervention.
40' - LALLANA SHOT - The Southampton captain turns brilliantly to take out Sylvain Distin and Leon Osman, but drags his shot wide.
55' - BARKLEY CHANCE - Ross Barkley meets Oviedo's cross from the left but is put off by Dejan Lovren's sliding challenge and shoots wide.
67' - SOUTHAMPTON PRESSURE - Luke Shaw brings the ball down superbly and sees his shot blocked, then Jay Rodriguez's follow-up is deflected just wide by McCarthy.
71' - GOAL: Everton 1-1 Southampton - Gaston Ramirez lets fly from 30 yards and the dipping ball flies between the outstretched gloves of Joel Robles.
74' - GOAL: Everton 2-1 Southampton - Lukaku grabs the winner with a powerful left-foot shot after classy build-up play from Pienaar and McCarthy.
81' - LUKAKU CHANCE - Brilliant from the Belgian who shimmies past three opponents but shoots just over.
Are Everton serious top four contenders? Roberto Martinez's men will end the year firmly in the mix for the Champions League places, but whether they have the strength in depth to keep pace with the leaders - and hold off Manchester United's likely second-half surge - remains to be seen.
MAN OF THE MATCH
Romelu Lukaku (Everton): Naming Lukaku man of the match is both predictable and boring, but it does have the virtue of being right. No current Premier League striker offers the same mix of power, skill and outright finishing ability.
EVERTON: Robles 5, Baines 7, Alcaraz 7, Distin 6, Coleman 7, McCarthy 7, Barkley 6, Oviedo 7, Osman 6, Naismith 6, Lukaku 8. Subs: Mirallas 7, Pienaar 7.
SOUTHAMPTON: K.Davis 7, Chambers 6, Lovren 7, Fonte 7, Shaw 6, Ward-Prowse 5, Cork 5, Davis 6, Lallana 7, Lambert 5, Rodriguez 6. Subs Clyne N/A, Ramirez 7, Gallagher N/A.
MATCH IN A TWEET