Jose Mourinho's third placed team are now two points adrift of Arsenal and one behind Manchester City, with Liverpool slipping down to fifth spot.
But Brendan Rodgers' side also took the lead and still lost at City on Boxing Day and once again they were unable to hold onto their advantage.
It took the Blues just 14 minutes to equalise as Oscar's shot hit Mamadou Sakho and bounced towards Belgium midfielder Hazard, who seized possession and blasted an unstoppable shot into the top corner of Simon Mignolet's goal.
And Chelsea struck again in the 34th minute when Cameroon striker Samuel Eto'o met Oscar's low cross with a prodded strike that eluded Mignolet's weak attempted save.
Sherwood had been frustrated by a 1-1 draw against West Bromwich Albion in his first match since being handed an 18-month contract to replace the sacked Andre Villas-Boas.
But the former Tottenham midfielder, who had overseen a win at Southampton during his brief spell as Spurs' caretaker boss, got the first victory of his official reign in emphatic fashion.
The north Londoners took the lead in the 37th minute when Ryan Shawcross blocked Emmanuel Adebayor's acrobatic shot with his arms in the penalty area.
Roberto Soldado stepped up to take the penalty and the Spain striker fired home for his fifth goal of the season and his fourth from the spot.
Belgium midfielder Mousa Dembele added the second for Spurs in the 65th minute with a low shot into the bottom corner. And Aaron Lennon delivered the knockout blow four minutes later, the England winger curled a cool finish into the top corner for his first goal since March.