MacKinnon extended his point streak to 14 games (nine goals, 16 assists) to begin the postseason, tied with Mark Messier (Edmonton Oilers in 1988) and Bobby Orr (Boston Bruins in 1970) for the second longest in NHL history. Bryan Trottier holds the record at 18 games for New York Islanders in 1981.
"You have to learn from what you did well every night and what you need to work on," MacKinnon said. "We're going to do that. We're going to review this game, find some things we need to improve on, but also build on the positives things. … Hopefully we can move on to the third round."
WATCH: [All Avalanche vs. Stars highlights]
Mikko Rantanen had a goal and an assist, and Michael Hutchinson made 27 saves for Colorado, the No. 2 seed in the West, which has won two straight.
Game 7 will be in Edmonton, the West hub city, on Friday (4 p.m. ET; USA, SN, TVAS).
Teams that win Games 5 and 6 after trailing a series 3-1 are 29-28 (50.8 percent) winning a best-of-7 Stanley Cup Playoff series.
"In terms of Game 7, it's my third one," MacKinnon said. "I guess I haven't won one yet. Looking to change that in a couple days here. Excited for the challenge. It's going to be the toughest game for us to win."
Miro Heiskanen scored, and Anton Khudobin made 20 saves for Dallas, the No. 3 seed.
"We all know what happened last year," Stars forward Tyler Seguin said. "We were in this position (up 3-2 against the St. Louis Blues in second round), a chance to win it in Game 6 on home ice. ... Game 7 we lost last year. So we have a chance to redeem ourselves. I definitely do think as an organization we've been trending in the right way, and this is the next step. It's going to be a big one for us in a couple of days."
Cale Makar gave the Avalanche a 2-1 lead at 7:48 of the second period, scoring top shelf after receiving a drop pass from Rantanen.