Tampa Bay's 11th straight victory -- the longest winning streak in the NHL this season -- broke the franchise mark of 10 set last season. Tampa Bay is the second NHL franchise to record a pair of double-digit winning streaks in a season, joining the Boston Bruins, who did so in 1929-30 and 1970-71.
Despite the milestone, Kucherov was disappointed in the Bolts' puck possession.
"I don't know. I don't think we played well today ... We have to improve a lot in our game because we have a lot of good teams ahead of us. I don't think we had a good effort today," Kucherov said after stealing the puck from MacKinnon and scoring in overtime.
Kucherov did have praise for Tampa Bay's Curtis McElhinney.
"We had a great goalie today," Kucherov said. "He had a heckuva game getting hit, but he stuck with it. He made some huge saves for us."
The Lightning have outscored teams 36-13 at even strength during their win streak, according to ESPN Stats & Information.
The game between two of the league's top teams had the feel of a playoff showdown, complete with momentum swings, hard hits and short tempers.
"It's not a team we play often, but when you have a good team like that and both teams want to win, it's going to boil over," said Cameron Gaunce, who scored one of Tampa Bay's three goals in the second period.
"He'll be out weeks," Avs coach Jared Bednar said.
Steven Stamkos had a goal for Tampa Bay in the second period that erased a 1-0 deficit, and McElhinney stopped 24 shots despite being bowled over by Colorado's J.T. Compher midway through the third period. That sparked the first of two brawls in a tense ending.
McElhinney crumpled awkwardly and lay motionless for a moment before he rose slowly. He was visited by a trainer but stayed in the game. Compher was called for interference.
McElhinney said he was fine physically and held no grudges.
"Honestly, I was kind of tied up. My arms were folded up under me. It wasn't a hit to the head or anything," he said. "It's a good hockey play. I like it when guys drive to the net, and I like the response from our team standing up for me. It's nice to see. It's hard hockey play on their part, and I don't have anything against that."
Another scuffle broke out after MacKinnon leveled Ondrej Palat cleanly in front of Tampa Bay's bench.
"I like the way that we hung in there. Good penalty kill at the end. In overtime, it comes down to a key save here and there and a big-time play from one of our big players," McElhinney said.
The Avalanche lost Rantanen when he was tripped into the boards at full-speed by Erik Cernak in the second period. Rantanen immediately left the ice and headed inside before the Bolts killed the power play.
Francouz stopped the first 11 shots he faced starting in place of Philipp Grubauer, who suffered a lower body injury in the Avs' 3-1 loss to the Kings on Saturday in the NHL Stadium Series at the Air Force Academy.
Palat sent a pass through the slot to Killorn as he skated toward the crease, and Killorn redirected the puck into an open net at 4:54. Gaunce scored his first goal since March 24, 2017, just 16 seconds later, with a shot from the point that beat Francouz on the short side.
Stamkos made it 3-1 when he came from behind the net and tapped in the loose puck sitting behind Francouz in the crease.
"Other guys have to step up," Bednar said. "It's a great opportunity. We have to carve out wins like we did earlier in the year. It's going to be tougher and tougher, but hopefully we can get those guys healthy and back to rejoin our team as soon as possible."
"It's pretty surreal this run we've been on the last couple of months," McElhinney said. "This 11-game run has been a lot of fun. It's special. It seems like we're going about our business, and it's not really so much about the streak."
Information from The Associated Press was used in this report.