Shea Theodore, Tomas Hertl and Ivan Barbashev each scored, and Jack Eichel had two assists for the Golden Knights (13-6-8), who won their third straight after losing their previous four.
"Akira made some good saves when we needed them," Cassidy said. "In the third period, I thought we played the right way. Special teams makes a difference. ... A couple of big kills and we get a power-play goal."
The Golden Knights finished 2-for-2 on the power play and 2-for-2 on the penalty kill.
Jacob Markstrom made 22 saves for the Devils (16-11-1), who went winless during their four-game homestand (0-4-0) and have lost seven of their past 10 (3-7-0). New Jersey, which lost 3-0 against the Dallas Stars on Wednesday, was shut out in consecutive games for the first time since April 13-15, 2021.
"It's frustrating right now," Markstrom said. "I mean, we just got off the ice, so it is frustrating. But I mean, it should be a 0-0 game coming into the last five minutes and it's not."
Asked if he thought he could have stopped some of the goals, Markstrom replied, "All of them."
The Devils, who were in first place in the Metropolitan Division on Nov. 30, are now in sixth.
"We need everybody on board," Devils captain Nico Hischier said. "I think we got to find our foundation, and it starts with just competing. I think it was a better game than versus Dallas, but we also got to find a way to score goals. Without scoring a goal, you're not winning."
New Jersey appeared score 8:45 into the first period when Hischier deflected in a shot from the slot, but the Golden Knights successfully challenged the play for offside when Timo Meier preceded the puck into the zone three seconds earlier.
Theodore gave Vegas a 1-0 lead at 19:47 of the first period on a snap shot from the right face-off circle that Markstrom missed to the far side.
Schmid made 11 saves in the second period. He denied Hischier off a 2-on-1 rush with Meier just 41 seconds into the second period.
Devils coach Sheldon Keefe could sense some frustration on the bench.
"You could see it wearing on the guys as the (second) period wore on, and they talked about it in the intermission," Keefe said. "But we're in the moment and needed to just focus on playing a great third period. But Vegas did a good job in the third and we didn't have the same level of jump."
Hertl extended it to 2-0 with a power-play goal on a redirection from the high slot at 15:36 of the third period.