The Ivorian's 100th goal for the club secured a vital three points while Tony Pulis will no doubt rue the brainless behavior of his frontman
Stoke came into the game having failed to win a league game against Chelsea 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 Juan Mata's through ball to net his 100th Chelsea goal.
Di Matteo decided to give John Terry his first start since undergoing knee surgery, replacing David Luiz at the heart of the defense.
Frank Lampard also returned to the lineup but Spaniards Juan Mata and Fernando Torres were consigned to the bench alongside Michael Essien.
The visitors were without Peter Crouch and there was also no place in the squad for Matthew Etherington, Stoke's match-winner in its last game against Norwich.
The hosts began encouragingly, pressing Stoke deep and forcing an early mix up between Ryan Shawcross and goalkeeper Asmir Begovic that saw the center back's header land on the roof of his own net.
Chelsea continued to press and Gary Cahill found room to bring the ball from defense. From 20 yards, the January signing hit a swerving right-footed strike that required a watchful Begovic to palm the ball behind for a corner.
But as the hosts verged on opening the scoring, John Walters carved a chance of his own. Chasing a long ball, the Irish forward got away with tripping Terry as the two came together on the halfway line.
Walters reached the loose ball and found himself with just Cahill to beat. Perhaps showing a lack of confidence, he saw his shot blocked before finding room past Cahill to slice the rebound wide. It was their best chance of the first half.
Walters' strike partner Fuller – starting his first Premier League game in over a year – fared even worse as he received his marching orders after just 25 minutes.
Fuller 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. It was a simple decision for Andre Marriner to make.
The visitors, so renowned for their set-piece expertise were again surprisingly lax in their defensive marking allowing Terry to meet another excellent Lampard delivery.
The corner, moving away and dipping beyond the Stoke defence was headed into the ground and onto the crossbar by Terry.
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, the main protagonist of the first period, who pounced on a loose clearance in the visitor's box and smashed a half volley against the crossbar as Di Matteo's team closed the half on a high.
Di Matteo replaced Ivanovic with Luiz after the break, the Serb presumably feeling the after-effects of the Fuller stamp.
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 tip 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.
Stoke came close to equalizing with 15 minutes to play as midfielder Andy Wilkinson showed ingenuity to attempt a 40-yard lob over Petr Cech.
Fortunately for the scampering Chelsea keeper, the impressive attempt drifted marginally wide.
As the game neared it's 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.
It may not have been pretty but Di Matteo's reign has now yielded two wins from two games. Lampard and Mata looked the two best players for the Blues while Tony Pulis will rue the inclusion of Fuller and point to his dismissal as the decisive factor in this narrow defeat.
In truth, it could have been far heavier for the Potters.