Everton are five points behind leaders Arsenal while Southampton remain ninth after a disappointing end to 2013.
Mauricio Pochettino's side had been third heading in November's fixtures but just two wins in 10 league games has seen them slide down the table.
Everton, who were missing Tim Howard, Phil Jagielka and Gareth Barry, led at the break courtesy of Coleman's wonderful strike - his fourth goal of the season.
The Republic of Ireland defender collected the ball wide on the right and easily cut inside James Ward-Prowse before advancing into the area and firing a stunning shot across keeper Kelvin Davis and into the top right hand corner of the goal.
Mann on the match
Alistair MannBBC Match of the Day commentator
"Everton end the year with just one home defeat in 2013 as they bounced back immediately from their defeat by Sunderland on Boxing Day. They produced two goals of real quality that sealed this game.
"Southampton had their moments and they will reflect on their missed opportunities as they head back south."
It was the only highlight of an otherwise turgid first half, although Ross Barkley had earlier side-footed Coleman's cross straight at Davis.
At the other end Adam Lallana had Southampton's best chance of the half but dragged a left-foot volley wide after showing neat footwork to create the opportunity.
Everton felt they should have had a penalty when Dejan Lovren shrugged Steven Naismith off the ball, while Rickie Lambert fired a tame half volley straight at Robles from 20 yards.
After the break Southampton captain Lallana was prevented from converting Luke Shaw's pass by a last-ditch tackle from McCarthy.
Bryan Oviedo found space on the left but his cross was side-footed wide by Barkley from close range while at the other end Jay Rodriguez went close for Saints as his shot from the edge of the area was deflected wide.
Saints progress pleases Pochettino
Ramirez's introduction galvanised Southampton and within four minutes of him coming on they were level. The Uruguay international picked the ball up midway inside Everton's half before advancing and unleashing a fierce, swerving shot that went through the arms of Robles.
The goal stunned Goodison Park but the home fans were soon celebrating their side regaining the lead with Lukaku finishing off a good break involving Steven Pienaar and McCarthy.
Lukaku hammered home first time from 12 yards and went close soon after with a strike from the edge of the area that fizzed over Davis' crossbar.
Davis was then forced into a smart low save from Lukaku's shot from the penalty spot as Everton ended 2013 with just one defeat at home, and atoned for their Boxing Day defeat by Sunderland in the process.
Everton boss Roberto Martinez:
"It was a completely different test to the one we had on Boxing Day. Southampton are a very god side and we knew that and we had to be perfect in our performance and the two goals were of outstanding quality.
"To see the way we got the winning goal was very satisfying and the nature of the victory was also pleasing considering the players we had out.
"We defended well and had real concentration which we needed against Southampton
"There was nothing Joel Robles could do (about the goal). The swerve in that ball from Gaston Ramirez he made it impossible for him.
"I couldn't be happier. We need the squad to be stretched and we looked like a solid unit."
Southampton manager Mauricio Pochettino:
"I thought it was a great game, both teams played positive football, it's a shame we did not get a positive result but that is football.
"We did have great chances it's shame we did not take the lead and a shame we leave with nothing.
"We are aware Everton are a side who play attacking football so from that point of view I enjoyed it, but I also suffered it as we did not get anything from the game.
"We are happy with how the team is progressing. We fully believe in the academy players and that is the project at Southampton. We just need to give them time to adapt."
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