The Blues won the first match of their far east tour in Kuala Lumpur but, as in their victory at Portsmouth just over a week earlier, they were far from convincing on Thursday.
And, like at Fratton Park, they needed an own goal to avoid a goalless draw in a match that saw new manager Andre Villas-Boas again play two entirely different XIs in each half.
The winner arrived 12 minutes from time when Drogba won a free-kick, which he took and smashed against the post, only for the ball to hit goalkeeper Mohd Izham Tarmizi and spin back towards the line.
The substitute thought he had retrieved the ball in time but the goal was controversially awarded.
Otherwise, Chelsea struggled against a side who conceded 10 times against recent tourists Arsenal and Liverpool.
Playing in what was extreme heat in front of a packed 84,980, the visitors began the match with captain John Terry, Drogba and Ashley Cole on the bench, and Fernando Torres spearheading a 4-3-3 formation.
The Spaniard missed an early chance, while Frank Lampard could easily have opened the scoring in the 17th minute when he was gifted the ball 10 yards out and stabbed wide.
Ryan Bertrand was forced off with a knock after 38 minutes before Lampard sent another shot wide and Yossi Benayoun and substitute Patrick van Aanholt also went close.
Chelsea's second-half team did not fare much better and were fortunate not to fall behind with a quarter of the game remaining when Syahrul Azwari blazed over after being played through.
Terry twice headed off target from a Drogba free-kick and Yury Zhirkov corner, moments which sandwiched a good chance for Daniel Sturridge, whose left-foot curler was palmed away by Mohd Farizal Marlias.
Drogba then looked to have spared any blushes Chelsea might have had, but the hosts should have levelled with six minutes left, Thamil Arasu wasting the chance to his and his team-mates disbelief.
Villas-Boas will be hoping for an improved performance in Sunday's game with Thailand All Stars in Bangkok, before heading to Hong Kong for the Barclays Asia Trophy.