With 4 minutes remaining and the score tied 2-2, the Leafs' Tyler Bozak forced a turnover in the Lightning's zone.
Phil Kessel corralled the puck and sent it to the right circle, where Van Riemsdyk fired a wrist shot past Ben Bishop.
Bernier made 13 of his stops in the final period, including a scintillating glove save on Martin St. Louis with 3:17 left.
Nazem Kadri scored twice for Toronto, which halted a two-game skid.
Mark Barberio and Matt Carle scored for the Bolts.
Bishop finished with 23 saves.