The opening set was a scrappy affair with both players struggling to hold serve in the early stages, although Radwanska eventually managed to get a foothold on proceedings to edge ahead at 4-3.
Sharapova did well to break serve for a fourth time in the eighth game to level up, however, eventually going on to see out the set.
It looked to be a far more straightforward second set for the world number two, but after racing into a seemingly unassailable 5-1 lead, she let her guard slip with Radwanska taking it to a tie-break.
Despite blowing one set point the Polish pro held her nerve to take the match into a decider.
Sharapova managed to save two break points as games went by way of serve in the third set, and eventually found a break of her own, which was enough to clinch the contest.