Dallas had a 3-2 lead before Roope Hintz scored on the power-play at 7:30, and Denis Gurianov made it 5-2 at 8:02 when Avalanche defenseman Cale Makar misplayed the puck behind the net and it bounced off Francouz.
"It just seems like when one team gets one goal, it kind of gives them a boost," Stars captain Jamie Benn said. "We found a way to get three quick ones early there (in the first period). They're a good team, they are going to battle back. … I'm not sure why it's going back and forth like this, but it is and you've just got to handle the momentum as it comes and not get too high, not get too low."
WATCH: [All Avalanche vs. Stars highlights]
Radek Faksa had a goal and two assists, and Hintz and John Klingberg each had a goal and an assist for Dallas, the No. 3 seed in the West, which scored three power-play goals.
Teams with a 3-1 lead are 284-29 (90.7 percent) winning a best-of-7 Stanley Cup Playoff series, including 6-0 in the first round this season.
Game 5 is in Edmonton, the Western hub city, on Monday (9:45 p.m., ET; NBCSN, SN, TVAS).
Valeri Nichushkin scored twice for Colorado, the No. 2 seed in the West. Pavel Francouz allowed five goals on 26 shots before being replaced by Michael Hutchinson 8:02 into the third period. Hutchinson made three saves in his playoff debut.
The Stars scored three times in the first 10:45 of the game.
Klingberg gave Dallas a 1-0 lead after Francouz was unable to secure a shot by Faksa at 6:18.
"A lot of players are feeling really good about their game right now and that's why we're such a confident group," Kilngberg said. "… Something that we were talking about to start of camp in August, we wanted the D to be more involved, get more O-zone time, and that's one of the keys to why you're seeing more offense."