Van Riemsdyk (third playoff goal) also had an assist. Tyler Bozak (2), Connor Brown (1) and Andreas Johnsson (1) also scored, and Frederik Andersen made 42 saves for the Maple Leafs, who trail the best-of-seven series 3-2.
Game 6 is Monday in Toronto.
David Backes (2), Sean Kuraly (2) and Noel Acciari (1) each scored goals for the Bruins, but goalie Tuukka Rask allowed four goals on 13 shots before being replaced by backup Anton Khudobin (eight saves).
Boston star center Patrice Bergeron returned after missing Game 4 with an upper-body injury. The Selke Trophy finalist did not record a point in 20:57 of ice time after totaling five assists over the first three games.
Toronto was bolstered by the return of Nazem Kadri, who was suspended for the last three games after his hit to Boston's Tommy Wingels in Game 1. Kadri had an assist in 13:58 of ice time.
Leo Komarov (lower body) did not play for the Maple Leafs despite deeming himself ready to return after missing Games 3 and 4.
Brown and Johnsson each scored their first career playoff goals -- at 6:36 and 10:12 ,respectively -- of the first period as Toronto carried a two-goal advantage into the first intermission despite being outshot 15-6.
Backes scored 16 seconds into a Bruins' power play with 10:15 remaining in the second after a Mitch Marner tripping penalty. Toronto answered with 9:24 left on Bozak's goal, and van Riemsdyk's power-play goal with 8:05 to go chased Rask.
Acciari's goal 5:56 into the third made it a one-goal game.
The Bruins are seeking their first playoff series victory since the 2013-14 season, while the Maple Leafs haven't prevailed in a series since 2003-04.
The winner of the series will face Tampa Bay in the conference semifinals.
--Field Level Media
Toronto | Boston | |
Tyler Bozak 2 | Points | Noel Acciari 2 |
Tyler Bozak 1 | Goals | Noel Acciari 1 |
Tyler Bozak 1 | Assists | Torey Krug 2 |
James van Riemsdyk 1 | Power Play Goals | David Backes 1 |
N/A | Short Handed Goals | N/A |
Frederik Andersen .933 | Save Percentage | Anton Khudobin 1.000 |
Frederik Andersen 42 | Saves | Tuukka Rask 9 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Toronto | 21 | 4 | 1-1 | 5-6 | 16 | 31 |
Boston | 45 | 3 | 1-6 | 0-1 | 6 | 35 |