Lumme knocked in the rebound of a slap shot from Pavel Bure that Calgary goaltender Dwayne Roloson couldn't control.
Flames forward Valeri Bure hit the post and was stopped by Vancouver goalie Sean Burke on a point-blank shot in overtime.
Hnat Domenichelli scored on a penalty shot while Marty McInnis, Andrew Cassels and Michael Nylander also scored for Calgary. Brad May, Donald Brashear and Markus Naslund also scored for Vancouver.
Domenichelli scored the only goal of the first period when he was awarded a penalty shot after being hauled down by Vancouver defenseman Adrian Aucoin while on a breakaway.
Domenichelli scored his fifth goal in four games since being recalled from Saint John of the AHL when he moved in on Canucks goalie Arturs Irbe and snapped home a wrist shot low to the stick side.
May evened the scored before the Flames took a two-goal lead on goals by McInnis and Cassels. The third goal, at 11:02 of the second period, prompted Vancouver coach Mike Keenan to replace Irbe with Burke.
Vancouver came back when Donald Brashear scored his sixth goal by banking a shot off Roloson and into the net.
Naslund scored to tie it at 3-3 before Nylander beat Burke on a breakaway to give Calgary the lead again.
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