This match was fitting for what has been a wildly unpredictable women's tournament but ultimately it was Barty who steadied her nerves in time to clinch a 6-7 (4) 6-3 6-3 victory and set up a clash with 19-year-old Marketa Vondrousova on Saturday.
Anisimova won just three points in the first five games but turned things around to win six games in a row and then take the set on a tie-break.
The young American, who had knocked out defending champion Simona Halep in the quarter-finals, then moved into a 3-0 lead in the second set only to lose six games in a row.
The decider was less wild but four consecutive games for Barty from 1-2 put her on the brink of victory and she served it out at the first time of asking, taking her third match point.
Barty took a break from professional tennis as a teenager after finding the pressure too much and spent a spell playing professional cricket, and this is the most remarkable chapter yet in her comeback.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies