After a virtually anonymous 79 minutes, Drogba reacted sharply to capitalise on some indecisive Portsmouth defending to meet substitute Ricardo Quaresma's dangerous cross and fire home the winner.
The home side had wasted a glorious chance ten minutes earlier when Niko Kranjcar connected with Peter Crouch's centre but the Croatian skewed his effort wide.
A lively first half saw both sides trade blows as Drogba was inches away from connecting with Ashley Cole's driven cross before Portsmouth goalkeeper David James denied the Ivorian after a clever chip pass from Florent Malouda.
Chelsea's dominance in midfield grew as the half wore on and Frank Lampard had a series of long distance shots that either flew wide or were denied by James.
James was not the only goalkeeper forced to earn his wages as five minutes before the break, Petr Cech was at full-stretch to deny Sean Davis' thunderous low drive.
As the weather worsened in the second half so did the football and the game looked destined for a stalemate unless someone could conjure a moment of magic.
Portsmouth striker David Nugent turned John Terry only to be denied by the imposing stature of Cech.
And the home side came so close to putting their noses in front when Chelsea threw all ten outfield players forward, neglecting to mark Peter Crouch, and when a long clearance up field found its way to the England striker he galloped forward with purpose before picking out Kranjcar but again the Croatian's finish was tame.
But with ten minutes to spare, Quaresma jinked his way down the right-hand side and although his near-post cross was intended for Michael Ballack, the German missed the ball altogether for Drogba to profit.
After the full-time whistle, Portsmouth confirmed that caretaker management duo Paul Hart and Brian Kidd are to stay in charge until the end of the season.
The pair were appointed following the sacking of Tony Adams at the beginning of February and under their leadership the south coast club have won one, drawn one and lost one of their three games.