The German came through 6-4 2-6 9-7 to set up a clash with Marion Bartoli in Saturday's final.
There was little to separate the two players in the early exchanges but it was Lisicki who made a crucial break in the seventh game, moving 4-3 ahead before holding serve to claim the first set.
Radwanska improved in the second set, dominating on her own serve and breaking Lisicki on four occasions on her way to taking it 6-2.
The Polish player broke her opponent again in the opening game of the third set, but Lisicki fought back with a break of her own in the sixth to level the scores.
Lisicki broke to move 5-4 ahead and have the opportunity to serve for the match, but Radwanska took the game with her fourth break point to make it 5-5.
The number 23 seed broke Radwanska once more before serving out the match to book her place in the final.