Jori Lehtera also scored for the Blues, and Jake Allen stopped 22 shots — including 14 in the third period.
Ryan Ellis had a goal and an assist and James Neal also scored for the Predators, who had their franchise-high five-game postseason winning streak snapped. Pekka Rinne finished with 17 saves.
Game 3 is Sunday at Nashville, Tennessee.
Tarasenko's game-winner came on lucky bounce. Jaden Schwartz led the rush and initially tried to pass it to Carl Gunnarsson, but the pass was off the mark and bounced off of Gunnarsson's foot right to Tarasenko's stick.
It was the first lead for St. Louis in 116:09 of the series.
