Avalanche forward Parker Kelly blindly passed the puck into the middle of the zone, where Pinto intercepted it and beat Scott Wedgewood blocker side from the slot.
The goal came after Drake Batherson had tied it 3-3 with 3:56 remaining in regulation, poking in a rebound in the crease after Jordan Spence's shot trickle five-hole on Wedgewood.
Tim Stutzle also scored for the Senators (12-6-2), who are 3-0-1 in their past four games. Linus Ullmark made 25 saves in his return after missing nine games with a lower-body injury.
Artturi Lehkonen, Parker Kelly and Gabriel Landeskog scored for the Avalanche (11-6-3), who have earned at least a point in four straight games (2-0-2). Wedgewood made 22 saves.
Avalanche forward Nathan MacKinnon and defenseman Cale Makar each left the game in the second period with a lower-body injury. MacKinnon left after trying to reverse-hit Senators defenseman Artem Zub. Makar, who exited practice early on Sunday, took a shift at 10:44 that lasted only four seconds before heading to the locker room. He briefly returned for a 23-second shift that ended with 5:20 remaining, but stayed on the bench for the rest of the period.
Pinto gave the Senators a 1-0 lead at 7:11 of the first period. He blocked Brent Burns' shot at the left point, won a race to the puck with Noah Juulsen in the right circle, and beat Wedgewood five-hole despite the Avalanche defenseman breaking his stick while attempting to prevent him from scoring.
Stutzle made it 2-0 at 13:13. Zetterlund battled with Makar for the puck behind the net before pushing it out front to Stutzle, who slid a backhand past the diving glove of Wedgewood and sliding body of Devon Toews.
Lehkonen cut it to 2-1 at 18:04 of the second period, beating Ullmark from between the circles for a power-play goal.
Kelly scored a short-handed goal to tie the game 2-2 at 3:54 of the third period. He intercepted a pass in the defensive zone, slowly skated up the ice on a 2-on-2 rush, and shot short side past the blocker of Ullmark.
Landeskog then gave the Avalanche a 3-2 lead with a power-play goal at 10:03 of the third, finishing a one-timer in the low slot off a feed from Brock Nelson.
