Chris Stewart scored 45 seconds into overtime and rookie Jake Allen made 27 saves.
The Blues return home for three straight beginning Tuesday vs San Jose after dropping three of five on the road.
St. Louis falls 6-5 on home ice, but still notches a point in standings.
Jason Blake scored the tiebreaking goal from behind the St. Louis net with 5:54 to play, and the Ducks rallied from a third-period deficit.
St. Louis has won two straight in the series and a 3-1 victory over Anaheim on March 8 is part of the club’s current 10-2-1 surge.
Patrik Berglund scored the go-ahead goal in the third period and Jaroslav Halak made 24 saves for his career-high seventh straight win to lead the Blues to a 3-1 victory over the Anaheim Ducks.
Francois Beauchemin, Corey Perry and Bobby Ryan scored during a 4:23 span of the third period, and the Anaheim Ducks beat the St. Louis Blues 4-2 on Sunday night.