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The Canadian, 20, will now meet French Open runner-up Simona Halep for a spot in Saturday's final at the All England Club.
Bouchard saved four break points during a tightly-contested opening set before going on to close it out 6-3 against the ninth seed.
She then opened up a 4-1 lead in the second thanks to two breaks of the Kerber serve, but the German dug her heels in to claw one of the breaks back.
However, the youngster was able to hold her nerve and seal the win 6-3 6-4 to make the last four at SW19.