Victor Anichebe capped a his return from injury by snatching a late winner at West Brom.
The Nigerian forward has been missing for four months with a groin problem and emerged for his first action since August as a second half substitute.
And when he pounced on a loose ball in the Albion area and slammed it in with six minutes left it sparked wild scenes among the travelling Evertonians.
More than a few were probably nursing hangovers but the Blues' first victory of 2012 will have aided the recovery of even the most severe post-boozing haze.
The first part of the game bore the same lethargy millions of revellers would be feeling after their New Year celebrations and it took a while for both sides to get going.
The first chance was crafted by Chris Brunt but Shane Long couldn't couldn't stretch his neck enough to divert the ball on target 18 minutes in.
Everton weren't creating much from open play but looked a real danger from set pieces and in the 24th minute Louis Saha's flick caused problems and Ben Foster blocked from Rodwell after making a mess of his original attempted claim.
Five minutes later Baines crashed a left-footed effort from the angle of the box right into Nicky Shorey.
After another deal ball delivery Phil Jagielka's header back into the box fell to Saha but the Frenchman screwed the effort wide.
Then the defender himself lifted an effort over the bar with the Baggies defence all over the place again.
Rodwell flashed the next Baines centre just wide then Peter Odemwingie blasted over at the start of the second half.
John Heitinga's touch denied the same player a clean strike of the ball 10 minutes into the second period and soon after Moyes boosted his attack by bringing Magaye Gueye on for Rodwell.
Victor Anichebe and Denis Stracqualursi offered further reinforcements not long after and their introduction was key.
Emboldened and in a more attacking shape, Everton stepped up the pace and Gueye lashed straight at Foster.
Anichebe's dangerous centre was cleared from the toe of Osman but then with five minutes left, the Toffees struck.
Tony Hibbert was released down the right and with Stracqualursi occupying the home defence, the ball fell to Anichebe who made no mistake.
