The Stars pulled within 3-2 in the best-of-seven Western Conference final with game six set for Monday at Dallas. A seventh game, if needed, would be Wednesday in Vegas.
The victory denied, at least temporarily, the host Golden Knights their second trip to the Stanley Cup Final in the club's six-season history.
The Stars are trying to become only the fifth team in NHL history to rally from a 3-0 deficit to win a best-of-seven series, and the first since the 2014 Los Angeles Kings did it in the first round.
"We feel good. We have a lot of fight in that room," Dellandrea said. "When we were down three we just kept focused, one game at a time, one period at a time.
"We're keeping our eyes pretty forward and narrow here, taking it slow, one day at a time. We've got a lot of confidence in that room."
The Stars took their first lead of the contest at 3-2 with 9:25 remaining in the third period on a sharp-angled shot by Dellandrea.
The 22-year-old Canadian centre fired a puck that deflected off Vegas defenseman Alex Pietrangelo's stick and went under the glove of Golden Knights goaltender Adin Hill and just inside the left post.
Dellandrea made it 4-2 with 7:58 remaining in regulation time when a loose puck bouncing in front of the goal landed on his stick and he fired it past Hill to give the Stars their biggest lead of the series.
It was the first multi-goal NHL game for Dellandrea, who managed only nine markers in the regular season, and his first go-ahead goal in an NHL third period.
"It's exciting," Dellandrea said. "Our line was working good all night. Felt good for sure.
"We've got bigger things we want to accomplish. This is a big win. We get to go back home and have another opportunity. We've been through a little bit of adversity this round."
Dallas captain Jamie Benn missed the contest while serving the second of a two-game suspension for a cross check of Vegas captain Mark Stone in game three.
"A big message in the room is we want to get Jamie back, we want to get our captain back," Dellandrea said. "We focused on that and we've got him back."
Either the Stars or Golden Knights will face the Eastern Conference champion Florida Panthers, who swept Carolina in the other semifinal series.
STARS ANSWER QUICKLY
Ivan Barbashev opened the scoring for the Golden Knights after 13:36 of the first period.
The 27-year-old Russian centre took a pass from Jack Eichel, came in from the left side, switched the puck from his backhand to his forehand as he skated across the front of the goal and fired the puck past sprawling Dallas goaltender Jake Oettinger for a 1-0 Vegas lead.
Luke Glendening answered for the Stars only 1:48 later on a tip-in off an assist from Thomas Harley to lift Dallas level. It was the second goal of the playoffs for the 34-year-old American centre.
Vegas fired the first six shots on goal but Dallas outshot the Golden Knights 13-10 in the first period.
Chandler Stephenson put Vegas back on top 3:20 into the second period, taking a cross-ice pass from Shea Theodore and firing a quick shot high over the glove of Oettinger.
Again the Stars answered quickly, with Jason Robertson netting the equalizer only 2:09 later, flicking a wrist shot past Hill.
