Heinen scored on a one-timer from the right circle off a pass from Adam Henrique on the rush to cut the lead to 3-2 at 14:06.
The Golden Knights went back ahead by two goals before the end of the period after the Ducks were called for too many men on the ice.
Stone scored 18 seconds into the power play on a breakaway that was initiated by Fleury to make it 4-2 at 18:13.
"The unfortunate thing is, we talk about it a lot, every moment in the game is critical," Eakins said. "We had a guy jump too early on a line change and we missed an assignment on our penalty kill. It's too bad because our penalty kill has been on quite a run lately (23-for-26, 88.5 percent in the past seven games), and those two moments were critical.
"We had just scored to come back in the game to make it a one-goal game and, boom, two mental mistakes, and now you've got to play two-goal catch-up against an elite team."
Alex Tuch scored into an empty net at 18:33 of the third period for the 5-2 final.
"Everybody is contributing on a different night," Stone said. "We're getting balance throughout the 12 forwards. For five, six games, [the top six forwards] were struggling and [the bottom six] were the ones that kept us going."
The Ducks went 0-for-4 on the power play and are 3-for-63 at home this season (4.8 percent).
"Our power play certainly isn't where it needs to be," Henrique said. "You need to get goals and produce there and create momentum."
NOTES: Golden Knights forward Reilly Smith did not take a shift in the final 13:28. DeBoer did not have an update but said Smith is day to day. ... Vegas forward Tomas Nosek had an assist playing 13:48 after being a late scratch Friday with an undisclosed injury. … Stone (three goals, five assists) matched his NHL career-high four-game multipoint streak from Dec. 13-19, 2019 (two goals, six assists). William Karlsson (five games, Nov. 16-25, 2017) is the only player in Vegas history with a longer streak. … Pacioretty has three goals and four assists during a four-game point streak. He is three points from 600 for his NHL career. ... The Golden Knights are 23-0-1 when scoring at least four goals in a game this season. ... Comtois has scored five of his 13 goals against Vegas. ... Henrique's assist on Heinen's goal was his 200th in the NHL. He has scored 397 points in 707 NHL games in 11 seasons with the Ducks and New Jersey Devils. … The Golden Knights won six in a row from Feb. 22-March 6.