The Clarets have now drawn four of their last five on their travels in the Premier League and have lost just once in eight — against Manchester City in mid-October.
Sean Dyche's side registered just one shot on target in the West Midlands having had just 35% of possession.
But the home side failed to make the most of their 16 shots on goal as the Clarets dug in for a share of the spoils.
Adama Traore was the closest to breaking the deadlock in the first half when countering from a Burnley corner and thumping the ball against the crossbar.
The Portugal international also had an opportunity to win the game in the second half, but Nick Pope's fine fingertip save kept the scores level.
Here are the ratings.
But the home side failed to make the most of their 16 shots on goal as the Clarets dug in for a share of the spoils.
5. Ben Mee 7
The skipper helped the Clarets reclaim their strong jaw with a stoic display at Molineux. Defended his box with a steely determination in Burnley's low block, won headers, closed down the space, but caught out for pace once or twice.
6. Johann Berg Gudmundsson 5
Picked up some promising positions in the final third, but wasn't able to deliver that killer moment. Didn't do enough on the ball to trouble Saiss, passes into the box generally picked out a Wolves shirt, and he was eventually replaced by Vydra.
7. Dwight McNeil 6
Had Burnley's best chance of the game when forcing Sa to save at his near post in the second half. Protected the ball well, without being able to travel into threatening positions, but worked hard to get back behind the ball when Wolves regained possession and Semedo slipped goal-side.
8. Jack Cork 6.5
Showed good strength on the ball in the middle of the park and helped the visitors get out of a few tight situations in their own half. Pressed well to take the sting out of the Wolves midfield and didn't take his foot off the gas from the first whistle to the last.