The stalemate at Molineux was their fourth draw on the road from the Clarets' last five games on their travels in the Premier League.
Only Manchester City have now managed to claim three points against Sean Dyche's side in the last eight fixtures.
But Burnley remain with a solitary win this term, at home to Brentford, and they never really looked like adding to that.
The home side were rather fortunate to still have 10 men on the pitch as Hee-Chan Hwang appeared to lash out at Matt Lowton in the first half.
Both players had gone to ground following an aerial challenge before the South Korean looked to throw an elbow in the full-back's direction.
However, referee John Brooks, making his debut in the top flight, opted to book the pair for their involvement in the squirmish.
The visitors had a very lucky escape of their own shortly after when Lowton's shot ricocheted into the path of Adama Traore.
The Portugal international broke a pace, leading a two v one counter, with only Charlie Taylor ahead of him and Raul Jimenez in support.
Traore chose to go alone, ignoring the run of his team-mate, before thumping an effort against the crossbar.
Wolves had the better of a dire second half, but only two of their 16 attempts at goal would be on target.
Hwang's effort, when going on the outside of Nathan Collins, took a nick off the defender and travelled agonisingly wide.
And Traore's daisy-cutter was kept out by Nick Pope, who dived at full stretch to produce a fine fingertip save.
The away side's only real chance of the half fell to Dwight McNeil, but Jose Sa saved well at his near post.
2.
The Clarets striker scored a hat-trick against Wolves last season, but didn't manage an attempt on target this evening.
