Manchester United's 3-1 defeat at Everton earlier in the day had given Chelsea the chance to open up a commanding gap over their title rivals.
It was an opportunity that they were not about to squander but it was a far from convincing display by Carlo Ancelotti's side.
Their one move of real class allowed Drogba to make the decisive breakthrough in the 40th minute as Wolves were left cursing themselves for failing to make some early pressure pay.
Drogba then made the game safe after 67 minutes as Chelsea recorded only a second win in their last seven games on the road.
Mick McCarthy's side had pegged Chelsea back in the opening skirmishes but, with Petr Cech denying Kevin Doyle and later Adlene Guedioura and Kevin Foley, Wolves were left without any reward for another improved performance.
Chelsea recalled skipper John Terry following his off-the-field problems and it proved a predictably uncomfortable afternoon for the former England skipper who was targeted by the taunts of the Wolves fans every time he touched the ball.
He almost gifted Wolves a 63rd-minute equaliser when he missed his clearance on the edge of the area to let in Foley but his blushes were spared by Cech.
Terry had the last laugh as Chelsea warmed up for Wednesday's Champions League clash against Internazionale by moving a step closer to winning the title with a victory that leaves Wolves still in the thick of the battle for survival at the opposite end of the table.
Wolves have now won just one of their last eight league games but they looked anything but a relegation-threatened side in the opening exchanges and would have taken a deserved 20th-minute lead but for the alertness of Cech.
Wolves had already threatened through Kevin Doyle and Foley before the quick thinking of the two Irishmen combined to create an excellent opening.
Doyle latched on to Foley's quickly-taken throw-in and homed in on goal only to see his shot palmed away at the near post by Cech.
Matt Jarvis and Dave Jones were also narrowly off target as Chelsea struggled to create a chance of their own - before Drogba struck five minutes before half-time.
All he had to do was tap the ball home from two yards as the hard work had been done for him by Michael Ballack and Yury Zhirkov.
When Zhirkov picked out Ballack the Russian raced into the area to collect a return pass and drilled his centre across the face of goal where Drogba was on hand to make no mistake from close range at the far post.
If Chelsea hoped to take charge after Drogba's sixth goal in five games, they were sadly mistaken.
Wolves continued to carry a threat and when a Jarvis cross picked out Guedioura at the far post in the 55th minute it needed a stunning save from Cech to retain Chelsea's advantage.
But Cech produced an even better stop eight minutes later from Foley following Terry's error. It was a decisive moment as Drogba then made the game safe with a goal that had McCarthy fuming on the touchline.
Cech's long clearance went straight to Drogba and he muscled his way past Christophe Berra before steering his shot beyond Marcus Hahnemann.