Clark took a pass from Chris Drury in the Toronto zone, skated to the right faceoff circle and ripped a slap shot into the top left corner of the net.
"I was thinking pass because I thought Dru was going to step up. But by the time I got a look, I just wanted to shoot as hard as I can," Clark said.
"On the overtime goal, I thought the puck was rolling," Toronto goaltender Trevor Kidd said. "He just made a good shot."
Although the Flames are all but certain to miss the playoffs for the seventh straight season, they continue to play well down the stretch with wins in five of the last six games.
Calgary twice erased one-goal deficits late in the third period, when the teams combined for three goals in a wild 2:13 stretch.
"The team is finding ways to come back and win games, and that's what we have to learn," said Flames captain Craig Conroy, who scored in the third period. "Those are things in the future that are going to make a big difference for this team. It is something we can draw from."
Just 35 seconds after Conroy brought the Flames even, Tie Domi poked in a loose puck to give the Maple Leafs a 3-2 lead with 5:10 left.
"It was a fun game to play," Iginla said. "It was physical, there were some fights. It had a little bit of everything. The Leafs are a good club, a physical, gritty team. We have a lot of respect for their team. They're going to be a tough team to play in the playoffs."
Kidd thought a penalty should have been called on Iginla's goal.
"(The referees) missed their guy holding Berg's stick as (Iginla's) coming out of the corner," Kidd said. "Unfortunately, (the referee) turned the cheek on that play and they ended up tying it up."
After defenseman Bryan McCabe and Dave Lowry traded goals in the first period, Nik Antropov's shorthanded tally gave the Leafs a 2-1 lead 5:15 into the second.
But Toronto could not hold on and dropped to 0-3-1-1 in its last five contests. The Maple Leafs are four points behind fourth-place Philadelphia in the battle for home-ice advantage in the first round of the playoffs.
"It was another game where we took a lot of penalties," Toronto captain Mats Sundin said. "It's tough to win a hockey game when you spend the amount of time we did in the penalty box. That was the biggest reason why we lost."
The Flames were 1-for-5 on the power play, while the Leafs were 0-for-7.
To make matters worse for Toronto, Doug Gilmour, who was making his first appearance since being reacquired from Montreal, left in the second period with an apparent knee injury and did not return. He exited the Pengrowth Saddledome on crutches.
"I hope it's not that bad, but I haven't heard," Sundin said. "I certainly hope he's going to be able to recover for the rest of the season. I hope it's not serious."
Following Antropov's goal, the contest settled into a defensive struggle, but things opened dramatically in the final minutes of regulation.
The Flames ended up with a 38-23 edge in shots.
With less than six minutes remaining, Lowry fed a cross-ice pass to Conroy, who broke in alone and flipped a backhander over the glove of a fallen Kidd, who made 34 saves.
Roman Turek, who stopped 20 shots, made a pad save on Sundin's blast from the point, but the puck trickled under his pads and stopped along the goal line. An unchecked Domi tapped it into an unguarded net for his 15th goal, giving the Leafs a brief 3-2 lead.