David Perron had a goal and an assist, Jordan Binnington picked up his franchise-record 12th playoff win and the Blues eliminated the San Jose Sharks with a 5-1 win in Game 6 of the Western Conference final Tuesday night.
Tarasenko, Brayden Schenn and Tyler Bozak also scored for St. Louis, which will face the Boston Bruins for the championship. Ivan Barbashev got an empty-netter with 2:15 left, Ryan O'Reilly had three assists and Binnington stopped 25 shots.
St. Louis won three consecutive games to advance to the franchise's first Cup Final since 1970. That series also pitted the Blues against the Bruins.
San Jose played without injured forwards Joe Pavelski and Tomas Hertl and defenseman Erik Karlsson. Injury attrition played a role for the Sharks, who played seven games in each of the first two rounds.
Dylan Gambrell scored his first career goal for San Jose, which lost for the first time in five elimination games this postseason. Martin Jones made 14 stops.
St. Louis grabbed control with a fast start.
Perron tipped in Sammy Blais' shot just 92 seconds into the game. Tarasenko made it 2-0 with a well-placed wrist shot at 16:16.
Tarasenko got his eighth goal of the postseason just seven seconds after San Jose forward Barclay Goodrow was sent off for tripping.
St. Louis D Vince Dunn missed his third consecutive game with an upper-body injury. He took a puck to the mouth in the first period of Game 3.
Game 1 is Monday night in Boston.