Less than a minute after van Riemsdyk's go-ahead goal, Lightning captain Martin St. Louis had an excellent chance for the equalizer, but was stopped by the left pad of Jonathan Bernier on a one-time shot.
Nazem Kadri scored twice in less than eight minutes to give the Maple Leafs (28-21-6) a 2-0 lead before the midway mark of the second period, but Matthew Carle and Mark Barberio responded for Tampa Bay (31-17-5) to tie it 2-2 after 40 minutes.
The win helped the Leafs avoid their fifth three-game losing streak of the season and halted the Lightning's three game win-streak.
Bernier made 40 saves in his first career start against the Lightning, while Bishop made 23 saves in the loss.
Kadri opened the scoring at 1:49 of the second period as his shot hit a Lightning player in front and fooled Bishop.
Then at 9:48, Kadri picked up his second of the night with a highlight-reel forehand-backhand deke to beat Bishop for his 14th of the season. It was Kadri's second multi-goal game of the season.
Ondrej Palat fed Carle with a no-look feed at 13:13 of the second, the Lighting blue-liner beat Bernier stick-side.
Barberio tied it four minutes later putting home the rebound off a scramble in front of Bernier for his fourth of the season and fourth in four games.
Toronto had three straight first period power plays, but had just three shots to show for it. The Lightning outshot the Leafs 11-6 in the opening 20 minutes.
The Leafs continue their three-game home stand Thursday against the Florida Panthers.
Notes: Canadian Olympic hopeful and Lightning star Steven Stamkos missed his 36th game recovering from a broken right leg. The Markham, Ont., native returned to practice Tuesday after missing Monday with discomfort. ... Maple Leafs forward David Bolland (ankle) participated in his first game day skate since suffering the injury Nov. 2. Toronto defenceman Mark Fraser was a healthy scratch for the 10th straight game while Paul Ranger was scratched for his 11th consecutive game. ... Six-time Canadian Olympic medallist Clara Hughes dropped the ceremonial puck prior to the game.