The Avalanche had a chance to win it on the power play late in the third period and again in overtime, but Hill made a couple of big saves, including stacking the pads on a one-timer from Cale Makar at 2:24 of overtime.
"We created some looks, we shot the puck and Hill made an amazing stop, a two-pad stack on Cale," Landeskog said. "No doubt when you have a two-minute power play in overtime you want to score, no doubt about that."
Following a 5-1 loss here to the Avalanche on Monday, Tocchet switched up all of his lines, and the Coyotes responded by scoring twice in the first five minutes after being held to 10 goals in their previous seven games.
Jakob Chychrun gave Arizona a 1-0 lead at 1:25 of the first period on a wrist shot just inside the blue line.
Goligoski then scored on the Coyotes third shot of the game to make it 2-0 at 4:52. It was his first goal since Feb. 6, 2020 (47 games).
"They probably outworked us tonight," Colorado coach Jared Bednar said. "They really wanted it. After that start, we're probably fortunate to get a point."
Landeskog cut it to 2-1 at 14:47 of the first when he kicked the puck to his stick to score off his own rebound on a power play. Rantanen tied it 2-2 by cutting to the net and scoring off a backhand pass from MacKinnon at 18:49.
Colorado's top line of Landeskog, MacKinnon and Rantanen has combined for 27 points (10 goals, 17 assists) in the past four games.
"Those guys are going to get their looks," Chychrun said. "They're obviously unbelievable players, so it was a huge comeback win for us."
NOTES:Colorado defenseman Bowen Byram missed the game with a lower-body injury and is day to day. … Johansson is still looking for his first win this season after he was 0-5-1 in seven games for Buffalo. … Colorado, which has scored at least four goals in six consecutive games, is 9-1-2 in its past 12 games. … Hill is the Coyotes' only healthy experienced goalie. Antti Raanta (lower body) was placed on injured reserve before the game, and Darcy Kuemper (lower body) hasn't played since March 8.