David Clarkson, Richard Panik and Roman Polak also pitched in as Toronto (10-8-2) scored early in the first and added three more in the second to snap a three-game losing streak in front of 19,089 fans at Air Canada Centre.
Alex Killorn and Steven Stamkos replied for Tampa Bay (13-6-2).
Van Riemsdyk went top shelf twice in the second period, beating Tampa Bay goaltender Ben Bishop over his glove at the 12:31 mark of the period and then again on the power play at 15:15. Van Riemsdyk's second goal gave the Leafs a three-goal cushion heading into the third.
The normally high-scoring Lightning couldn't break through Leafs goalie Jonathan Bernier, who redeemed himself after being pulled from Tuesday night's 9-2 loss to Nashville after giving up three goals on 12 shots over 20 minutes.
Against the Lightning, Bernier was beat on the rush when Killorn used Toronto defenceman Jake Gardiner as a screen and snapped home a short-handed goal to tie the game at 1-1 in the first. Stamkos scored one in close late in the third with the goalie pulled and just over four minutes to play.
Despite a late Lightning charge in the final minute, Bernier stood tall to record his sixth win of the season, stopping 26 of 28 shots.
At the other end of the ice, Bishop was hung out to dry on several occasions.
Toronto's second goal came as a result of a bad turnover by Tampa defender Matthew Carle, whose backhanded clearing attempt was easily picked off by Panik — the former Lightning forward — and promptly tucked past Bishop.
Van Riemsdyk was left all alone to do as he pleased with a rebound from a Phil Kessel wrister later in the period, electing to flip the puck past Bishop on the Leafs' fourth goal.
Polak put the puck in to the empty net to seal the win for Toronto.