Wolves, however, continued to dominate possession and knocked on the door once again on 12 minutes as Helder Costa whipped in a cross which was just too heavy for Willy Boly and Hart had to be alert to fingertip away.
Although Burnley did have the odd opportunity, with Phil Bardsley blasting over in the 23rd minute, the momentum was firmly with Nuno Espirito Santo's side, even though they could not break the deadlock come the half-time whistle.
However, the hosts' perseverance finally paid off when, just after the hour mark, Doherty cut the ball back into the middle for Raul Jimenez, who coolly slotted past the impressive Hart and into the bottom corner of the net.
Although Wolves failed to add to their solitary goal and even ran some risks in injury time when Gudmundsson forced a save from Rui Patricio, they finished strongly and saw out the game for all three points and a first home win of the season.
WOLVERHAMPTON WANDERERS (3-4-2-1): Patricio; Bennett, Coady, Boly; Doherty, Moutinho, Neves, Jonny; Costa (Traore 66'), Jota (Gibbs-White 88'); Jimenez (Bonatini 76')
BURNLEY (4-4-2): Hart; Bardsley, Tarkowski, Mee, Taylor; Lennon, Cork, Hendrick (Westwood 79'), Gudmundsson; Barnes (Vydra 56'), Vokes (Wood 70')