Marc-Andre Fleury made 21 saves and was denied his 30th win of the season for Vegas (31-23-4), which has lost a team record four in a row at home and six of eight overall.
"In my opinion, we give them three goals from our mistakes," Golden Knights coach Gerard Gallant said. "They played well; I give them credit. But when you give them three goals like that, you're not going to win many games."
After being outshot 16-6 in the first period, the Coyotes took a 1-0 lead at 9:38 of the second when Oesterle scored a power-play goal.
Galchenyuk made it 2-0 at 14:00 of the second on a breakaway.
"We weathered the storm when we could," Coyotes coach Rick Tocchet said. "I thought we had some big goals from some big guys at crucial times. That bend-don't-break defense helped us tonight."