David Moyes' side leapfrog visitors Wigan who will be disappointed to come away from Goodison Park with nothing after taking the lead and holding onto a draw for most of the game.
The visitors went ahead on the half hour mark through top scorer Franco Di Santo. It was another wonder goal from the forward, his shot from the corner of the box, bending around Tim Howard and into the top corner.
The goal came against the run of play with Tim Cahill and Seamus Coleman each seeing shots blocked at the other end but the home fans did not have to wait long for an equaliser. It took just two minutes for Everton to win a corner and Phil Jagielka headed in from close range after Tim Cahill's header came back off the crossbar.
Neither side could take control of the game following the two quick goals and this continued after the break. Leon Osman was a bright spark in the Everton ranks and his hard work and dangerous cross into the six-yard box deserved to be turned in by a team-mate.
Wigan came close on a couple of occasions through left-back Patrick Van Aanholt who saw long range efforts deflect wide and graze the crossbar but Tim Howard remained untroubled.
With the game heading towards a stalemate both managers tried their luck with substitutions and it was David Moyes' whose decisions paid off. Super-sub Vellios made an immediate impact when he latched onto a Tony Hibbert cross to powerfully head past Ali Al-Habsi before Drenthe wrapped up the points. A serious injury to Hugo Rodallega accounted towards a lengthy stoppage time and debutant Drenthe coolly slotted the ball past Al-Habsi in the 97th minute.