The teams totaled three goals in the first two periods, then combined for three more in a 5:05 stretch of the third.
Hoffman tied it 2-2 early in the third, scoring from a sharp angle down low to beat Budaj at 2:49.
Parenteau regained the lead for the Canadiens with a power-play goal from the point. Lehner appeared to make the save, but the puck trickled through his pads.
The Senators took advantage during a two-ma, 19-second power play as Chiasson scored on Mika Zibanejad's rebound to tie the score again at 7:54.