Rust tied it 1-1 at 16:22 of the third. After Francouz dove to try and poke the puck away, Malkin received a pass from Jason Zucker at the right post before centering the puck that caromed off Rust's skate and the pad of Francouz.
Letang came close to scoring the game-winner for Pittsburgh 25 seconds into overtime by chipping a shot on goal, but video review determined the puck did not cross the line.
"We have a lot of talented players. It's tough, sometimes, to tell them what to do," Letang said. "They see things that a lot of people don't see. But sometimes when you're not able to generate offense, you want to simplify, you want to put the puck at the net, be predictable for your teammate. Sometimes, it's good."
The Avalanche then had a power-play opportunity after Malkin was called for tripping Cale Makar at 1:21. Colorado had three shots on goal and eight shot attempts.
"I thought we did a great job keeping them to the outside," DeSmith said. "They had some one-timers, obviously. But we kept them out of the middle, kind of toward the flanks. Obviously, it's my job to stop those ones, [and] thankfully I did."