"That was my biggest win since my comeback from injury," she added having missed four months last year with a shoulder injury.
Sharapova claimed her ninth win in 11 matches against world number three Radwanska of Poland, but the statuesque Russian did not have things her own way, despite needing only one hour, 39 minutes to claim victory.
After a total of seven breaks at the start of the match, as the momentum swung back and forth, Sharapova finally won her first service game to take control of the first set.
"That was one of the key moments," she said after eventually needing eight match points to claim the win.
She will now face either Spain's Carla Suarex Navarro or Italy's Sara Errani in Saturday's semi-final.
"It'll be a tough game, they are both clay-court specialists," said the Russian.
Having won all four Grand Slams, Sharapova is bidding to claim a personal landmark this week in Stuttgart by winning a tournament three times in succession.
Victory bought an extra bonus for the Russian as failure to beat Radwanska would have seen Sharapova fall out of the top ten for the first time in three years.