"We can't keep throwing these points away," Flames defenseman Derek Smith said. "We're beating ourselves, and if we want to keep climbing the standings we can't let this happen again."
Calgary rebounded from a two-goal, third-period deficit when Bourque scored on a breakaway in the opening minute and Jokinen redirected Alex Tanguay's shot past Mathieu Garon during a power play with 3:12 to go in regulation.
Jokinen took the blame for Stamkos' goal after getting caught deep in the offensive zone.
"The overtime goal was my fault ... I should have stayed high," Jokinen said. "You put yourself in a position where you have a chance to win and get two points, then a mistake like that on my part, not playing smart hockey, cost us an extra point."
After Pyatt scored with 9:50 to go in the second, Malone gave Tampa Bay a 3-2 lead from the left circle just under 2 minutes later. Thompson made it 4-2 with 33.4 seconds to go in the period when his shot went into the net off Calgary defenseman Chris Butler's leg.
"We played two terrific periods," Tampa Bay coach Guy Boucher said. "What we saw there in the third is just a lack of confidence that stems from the previous games slipping away. The two big periods like that to start, getting five goals from pretty much all lines certainly is going to give us more confidence."
Calgary went ahead 2-1 when Iginla scored his 12th goal this season and 496thh of his career from the top of the left circle 1:57 into the second. The Flames' captain is two goals away from tying Glenn Anderson for 42nd place all-time.
Purcell put the Lightning ahead 1-0 during a power play at 5:11 of the first. Purcell sent the puck toward the net from a tough angle that went off goalie Miikka Kiprusoff's stick and then Butler's body.
Thompson (20 games) and Purcell (16 games) both stopped personal goal-scoring droughts
Stajan tied it 1-all with his first goal in 36 games, dating to March 12 against Vancouver, with 32.2 seconds left in the first.
This was just the third time Calgary has played a regular-season game at Tampa Bay since the start of the 2002-03 season. The Flames played four times in Florida against the Lightning in the 2004 Stanley Cup finals, which was won by Tampa Bay.
Jay Feaster, the Lightning's general manager in 2004, returned to Tampa for the first time as Calgary's GM. "It's big time weird, Feaster said. "This was home for a long time." ... Iginla played in his 1,137th NHL game, tying him for 129th place all-time with Cliff Ronning. ... Lightning D Mattias Ohlund, sidelined all season after undergoing surgery on both knees in October, still hasn't resumed skating and remains out indefinitely.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Mike Leggo, Mike Leggo Linesmen: Pierre Racicot, Jay Sharrers
Attendance: 17,241 (89.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Teddy Purcell (6)
(Power Play) Assists: Steve Downie, Dominic Moore
Matt Stajan (1)
Assists: Tim Jackman, Tom Kostopoulos
Jarome Iginla (12)
Assists: Olli Jokinen, Jay Bouwmeester
Tom Pyatt (3)
Assists: Ryan Shannon, Blair Jones
Ryan Malone (7)
Assists: Steven Stamkos, Victor Hedman
Nate Thompson (3)
Assists: Dana Tyrell, Victor Hedman
Rene Bourque (10)
Assist: Derek Smith
Olli Jokinen (9)
(Power Play) Assists: Alex Tanguay, Derek Smith
Steven Stamkos (19)
Assists: Eric Brewer, Steve Downie