The New Jersey-born Anisimova looked in fine form at the start of the match and produced a big serve that Keys could only dump into the net to win the first set in warm afternoon sunshine on Centre Court.
But that serving weapon, which earned her 20 aces in the last round to beat another American in Sofia Kenin failed to fire in the second set on Saturday. She had trouble with the toss and suffered breaks in the second and eighth games.
Keys, whose best performances at Wimbledon are two quarter-final appearances but who won the Eastbourne warm-up tournament on grass last month, grew in confidence and consistency.
The 26th seed, last year's Australian Open champion, won 76% of points on her first serve and produced 23 unforced errors to the 24-year-old Anisimova's 42.
A magnificent backhand pass secured her a break of serve in the fourth game of the decider and she won the match with a serve that Anisimova put wide.