Brendan Lemieux scored, and Henrik Lundqvist made 28 saves for the Rangers (13-10-3), who were 4-0-1 in their previous five games.
Vegas was 2-for-2 on the power play. The Rangers were 0-for-6.
"It comes down to special teams, not getting it done on the PK," Lundqvist said. "They made two good plays, but we need to find a way there. … I need to find a way to make that extra save."
Tuch gave Vegas a 1-0 lead at 1:34 of the first period when his shot got through Lundqvist and the goalie kicked it over the goal line with his left pad before Tony DeAngelo could pull it back. Video review confirmed the puck crossed the goal line.
Tuch said he did not know it went in.
"I celebrated kind of like that too," he said. "I put my hands up, down, up, down. The guys came over and told me they didn't touch it and it was in the net, so I'll take it."
Tuch made it 2-0 with a power-play goal at 3:50, scoring on a tip-in off a pass from Nate Schmidt out of the left circle. Vegas was on the power play because Brady Skjei was called for holding Tuch's stick at 1:52.
The Golden Knights outshot the Rangers 13-2 in the first 7:29.