Burnley were sharper and more committed but mid-table Wolves contributed to their downfall with some sloppy defensive work at an empty Molineux.
The away side took the lead in the 15th minute after Wolves defender Willy Boly misjudged a header and the ball fell to Wood. The New Zealand forward turned Conor Coady one way then the other down the right before firing the ball into the far corner of the net from an acute angle.
Burnley doubled their lead just six minutes later. Dwight McNeil seized on a sloppy pass from Adama Traore, crossing for Wood to tap home from close range. McNeil was again the provider as Wood completed his hat-trick shortly before half-time, heading home a corner.