The Blues, owners of the best record in the NHL, gave away a one-goal lead on three occasions and surrendered a pair of third-period tallies that handed the Ducks their second straight win.
It was a 2-2 game heading into the third and St. Louis took the lead on a power-play goal from David Perron 4:47 into the stanza.
Devante Smith-Pelly tipped in a shot 3 minutes later to again tie the contest and Blake put Anaheim in front for the first time all night.
Jaden Schwartz and David Backes each gave St. Louis the lead during the first two periods and Anaheim came up with tying goals from Cam Fowler and Nick Bonino.
The win went to Jonas Hiller, who made 34 saves. Jaroslav Halak gave up the four goals on just 22 shots.