Matt Grzelcyk scored the lone tally for Boston, slotting one past Jordan Binnington with 2:10 to go in the third.
O'Reilly was awarded the Conn Smythe Trophy as the playoff MVP.
St. Louis had a chance to clinch the Cup on home ice in Game 6, but the Bruins earned a 5-1 victory to set up the decisive match at TD Garden.
St. Louis appeared in the championship round for the first time in 49 years after defeating the San Jose Sharks in six games in the Western Conference Finals.
This series is the second time the two squads squared off with the Stanley Cup on the line. The first came in 1970 when Boston won the series 4-0.
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