With 25 seconds left on the clock in the extra frame, Jets captain Andrew Ladd sent a long backhand shot toward Avs goalie Semyon Varlamov, which Little deflected from the front of the net for his fifth goal of the season.
"Honestly, I didn't think I did," Little said. "But then I saw the replay, and if I did, I didn't feel it.
"I don't know, ask Laddy."
Ladd had scored his second goal of the season, and 100th goal with the Jets franchise, at 6:35 of the first period after redirecting defenceman Zach Bogosian's point shot through Varlamov's legs.
His assist was the 200th of his NHL career.
"I saw Lits at the net so I just figured we'd get some action there. You know, hope something lucky went in," Ladd said.
"I think at that point, you really don't want to mess around with plays up top so I thought it was the safe play and lucky it went in."
Jets goalie Ondrej Pavelec stopped 22 shots in regulation and overtime.
Jamie McGinn scored Colorado's goal on the power play with 18 seconds left in the first period. Varlamov faced 28 shots.
It was Winnipeg's (3-5-0) first game of the season that went to extra time while Colorado (2-4-3) has now lost three in overtime.
Winnipeg outshot the Avalanche 6-2 in overtime.
"I thought we had a lot of good chances in the first (period), we just didn't score on those ones," Colorado head coach Patrick Roy said. "Obviously, we had a few good looks also in overtime. (Gabriel Landeskog) had a chance there and then their goalie made a great save on that play. I thought it was a great game."
Roy had nothing but praise for his netminder.
"I think Varly knows he played a really good game," Roy said. "I don't think there's much to be said there. I thought we played well in front of him.'
Colorado defenceman Erik Johnson left the ice after being checked into the boards in the third period, but Roy said he hadn't talked to the trainer about his status.
Both teams had power-play chances late in regulation.
With 3:32 left in the game, Jets forward Mathieu Perreault was called for holding, giving the Avalanche their fourth power play of the game. Winnipeg then went on its third power play of the game after forward John Mitchell was called for tripping with 1:18 left. They had a shot blocked and another stopped by Varlamov. Pavelec also stopped a one-timer by defenceman Tyson Barrie.
The game wrapped up the Jets' five-game homestand, in which they went 2-3-0.
McGinn scored his goal with 18 seconds left in the first period when he got his stick on a rebound off Barrie's one-timer. It was just seven seconds after Bogosian was handed a double minor for high sticking Matt Duchene.
Barrie extended his point streak to four games (five assists, one goal) with the helper. Alex Tanguay also added an assist, putting him on a four-game point streak (3G, 2A).
Duchene said the Avalanche played hard and had chances, but the Jets neutralized their speed and skill.
"We easily could have won that hockey game," Duchene said. "Kind of a flukie one at the end there. I still don't know how it ended up in the net. Even their first one there, tipped by Ladd in the front."
Things got heated with 4:01 left in the second period after Jets forward Dustin Byfuglien checked Barrie hard into the boards. Mitchell then came at Byfuglien, who smashed him to the ice, too.
Mitchell was assessed four minutes for roughing and Byfuglien, who assisted on Little's goal, got a roughing minor.
Winnipeg heads out for a four-game road trip, starting Tuesday against the New York Islanders.
The Avalanche, who had a dominating 7-3 home win Friday against Vancouver, return home for a game against San Jose on Tuesday.