Pilar got to a loose puck in the right faceoff circle and fired it past goaltender Nikolai Khabibulin to extend the Maple Leafs' winning streak to four games.
"I knew two of their guys were behind the net," Pilar said. "So I took a bit of a chance and pinched, and it paid off. I've been trying to focus on my game defensively, so this is a huge bonus."
Brad Richards recorded two assists for the Lightning, who took a 2-0 lead into the third period and needed a confidence boost after conceding two goals in 18 seconds late in the final period of Sunday's loss to the New York Rangers.
"I thought the third period was going very well," Lightning coach John Tortorella said. "And then we stubbed our toe. As we go through these situations, we'll become better. It's all a test. We're still learning to get out of these jams."
Vincent Lecavalier put Tampa Bay back in front with a stunning individual effort, but Robert Reichel registered his third goal of the season with four minutes remaining to force overtime.
Khabibulin tried to prevent another defensive collapse by Tampa Bay, making 44 saves, but the Lightning dropped their third straight contest and are winless in four (0-3-1).
After Martin St. Louis knotted Friday's contest, Tampa Bay gave up two goals in the final 6:11 of a 5-3 home loss to Vancouver. On Sunday in New York, St. Louis put the Lightning ahead with 5:13 left, but they yielded the equalizer with 2:48 to play and the game-winner just 18 seconds later.
St. Louis and Fredrik Modin matched a team record by scoring 12 seconds apart to give the Lightning a 2-0 lead at the first intermission. Tampa Bay also tallied twice in 12 seconds on December 4, 1993 at Los Angeles and on October 31, 1996 against Philadelphia.
St. Louis scored his 15th goal of the season, joining four others with a share of the league lead.
Khabibulin was under siege but stopped all 19 shots in the second period to preserve the 2-0 lead. But he was surprised by Hoglund, who turned at the inside of the left circle and halved Toronto's deficit.
"We had a slow start and then a great second period," Sundin said. "Even though we didn't score any goals, we found our legs, hung in there and got a well-deserved two points."
"That's my job and I take pride in making those big saves," Belfour said. "I gave our team a chance to win, which was great. We really worked hard at trying to get our game back and when you do that, good things start happening."
The Lightning had made a habit of third-period comebacks, earning points in 11 games in which they were trailing.
"It's been our strength, the third period. We've been strong late in the games," Modin said. "And now we're making mistakes late in the games. We just have to get back to the way we were playing."
Sundin, who also assisted on the game-winner, has scored in consecutive games following a seven-game drought. On a 2-on-1 shorthanded rush, his blast from the right circle deflected off the stick of defenseman Pavel Kubina and past Khabibulin to tie it.
It took just 45 seconds for Lecavalier to put Tampa Bay back in front. He streaked down the right wing, cut in front of the crease, deked Belfour and slipped a backhander past the skate of the sprawled goalie.
"We still have confidence, we know we can win," Lecavalier said. "It's not like last year, where our confidence was shaky. It's just a matter of getting through the rough time we've had the last few games. It's been tough. But we'll get some big wins and come back."