Iginla was robbed by the glove of Roberto Luongo on a breakaway with 2:06 remaining in the third period, but the Calgary captain converted in the third round of the penalty-shot tiebreaker, scoring on a backhand-forehand deke.
Miikka Kiprusoff, who made 29 saves, turned away Mason Raymond's bid to assure the extra point for the Flames.
"It certainly wasn't pretty at times, but we battled for everything in that hockey game and deserved the two points," said Flames associate coach Craig Hartsburg.
Calgary notched its first home win over Vancouver since October 16, 2009. The Flames had dropped five straight at home to their Northwest Division rivals.
Luongo finished with only 16 saves for the Canucks, who were looking to sweep a four-game road trip.
"I thought we played a really good game tonight from start to finish. This was probably our best game of the road trip and we lost," said Canucks head coach Alain Vigneault.
Vancouver is all too familiar with the shootout as six of its last nine games have been decided beyond overtime.
Calgary jumped out to a 2-0 lead on goals by Mike Cammalleri and Roman Horak, with the latter lighting the lamp at the 2:41 mark of the second period.
But the Canucks rallied, beginning with Cody Hodgson banging home a rebound late in the middle stanza. David Booth pulled the visitors even at 8:04 of the third.
The Flames improved to 3-0-2 in February...Vancouver had its road winning streak snapped at five games...The teams entered play with identical 12-3-0 records within the division.