Ryan O'Reilly netted the other goal for the Avalanche, who won at home for the eighth straight time to set the franchise's longest win streak since the team moved from Quebec City to Denver.
"We were aware of the streak, coach told us about it before the game," Duchene said. "We're very appreciative, accounting for all the great teams that have been here before."
Jean-Sebastien Giguere made 29 saves, including four in the extra period, for the win, Colorado's fifth in six games with all six contests being decided by one goal.
The game-deciding goal came 3:38 into overtime after Duchene picked up a drop pass at the blue line and cruised down the left side of the offensive zone. As Duchene reached the corner, he threw the puck towards the net, where Garon had his legs spread a little too far apart and the puck caromed off his left foot and through his legs.
"He shot it off my pad about six inches from the post. I thought I had it," said Garon. "We're lucky to get the point tonight."
Tampa Bay struck first with just 1:51 left in the opening period when Kubina received a pass at the top of the right circle and swept a shot towards the net that snuck through the pads of Giguere.
But Colorado netted the equalizer at the midpoint of the second period with a Shane O'Brien shot from the right point that Garon thought he had in his equipment, but O'Reilly was there to grab the loose puck and backhand it into the net.
The Avalanche seemed to have scored the game winner with 47.9 seconds left in regulation, but the whistle had been blown by the referee before the puck crossed the line as Kubina was on the ground because of a high stick.
No penalty was called on the play, though, despite blood trickling down the right eye of Kubina, denying Tampa Bay a possible four-minute power play.
Colorado's franchise record for consecutive home wins is 10 by the Quebec Nordiques in 1983-84 and 1994-95...O'Brien's assist stretched his points streak to a career-high four straight games (0G, 4A)...Colorado closed out a four-game homestand with a 4-0 record, improving to 12-9-0 as the host this season...Tampa Bay fell to 6-12-3 on the road this year.