The Ivorian's 100th goal for the club secured vital three points whilst Tony Pulis' men will no doubt rue the brainless behaviour of striker Ricardo Fuller, who was sent off
The Potters came into the game having failed to win a league game against the Blues home or away since 1975 and matters were not helped by Ricardo Fuller's sending off for a crass stamp on Branislav Ivanovic in the first half.
Chances were hard to come by, but Chelsea's patience was rewarded in the second half as Drogba latched onto a Juan Mata through-ball to net his 100th Chelsea goal.
The hosts began encouragingly, pressing Stoke deep and forcing an early mix-up between Ryan Shawcross and goalkeeper Asmir Begovic that saw the centre-half's header land on the roof of his own net.
On the fourth minute Chelsea forged their first clear chance. An out-swinging Lampard corner was met by the unmarked Ivanovic and although the Serbian right-back connected well, it was a poor header, sailing just over the crossbar when it looked easier to score.
But as the hosts verged on opening the scoring, John Walters carved a chance of his own. The striker chased a long ball, the Irish forward got away with tripping Terry as the two came together on the halfway line, before shooting twice, failing to score on both occasions.
Walters' strike partner Fuller fared even worse as he received his marching orders after just 25 minutes. He chased a long pass and as Ivanovic slid to hook the ball to safety, the Jamaican reacted impetuously by deliberately stamping down on the Chelsea defender, prompting Andre Marriner to show him the red card.
Chelsea continued to search for the opener and Ivanovic, who was afforded far too much space, played a one-two with Lampard on the edge of the box leading to a looped header that was claimed by Begovic on his goal-line.
As half-time approached, Di Matteo made his first substitution, introducing the mercurial Mata for Raul Meireles.
But it was Ivanovic, who pounced on a loose clearance in the visitors' box and smashed a half volley against the crossbar as Di Matteo's team closed the half on a high.
The hosts continued to lack creativity in the final third and the only chances of the first 15 minutes of the second-half came from long-range efforts from Lampard, Luiz and Terry. The home support seemed notably more patient and were almost treated to a splendid Drogba goal as Begovic flew to his left and tipped the shot over the bar.
But it wasn't long until Drogba did find the net. Mata found room on the edge of the box and slipped the ball into Drogba whose first touch drew Begovic from goal. His second allowed him to round the Bosnian leaving an open goal for the 34-year-old to break the deadlock and bring relief to Stamford Bridge.
Lampard came close to doubling the lead minutes later but his fierce shot from 25 yards was smuggled away by the busy Begovic.
As the game neared its conclusion, Mata almost left the supporters with a final reason to cheer. His curling left-footed free-kick beat Begovic but rebounded back off the upright – the third time in the game the hosts had hit the woodwork.
Following today's game, Chelsea are fifth in the standings with 49 points, while Stoke sit 10th with 36.