Captain Mikael Backlund nearly ended it in regulation time, deflecting a Kevin Bahl point shot goalward with about a minute left to play in the third, but Kuemper got down quickly to get his torso to the puck, securing a point for both sides in the process.
Calgary had two glorious chances in overtime. Olofsson danced through everyone, nutmegging Artemi Panarin in the high slot before chipping the puck just wide of Kuemper's left post. Morgan Frost hit the pipe a minute later on a two-man breakaway with Joel Farabee, while at the other end, Panarin forced Wolf into a lunging save with about 10 seconds left in the extra session.
Frost scored the opener in the shootout for the Flames, a tally cancelled out by Panarin on L.A.'s second attempt.
That set up Sharangovich in round four. The winger strode in, tried to deke Kuemper out but lost the handle on the puck. Nevertheless, the disc glided beneath Kuemper's pad and into the back of the net, securing the victory for the home side.
Twenty of Calgary's 30 wins this season have come on home ice.