Adama Traore returned to Wolves' starting line up but continued to both entertain and frustrate as the hosts fired blanks.
Traore was recalled to Wanderers side after four games as a sub as Barcelona loanee Francisco Trincao dropped out.
The Spain international always carried a threat with his pace and direct running which had fans off their seats.
But yet again Traore's decision-making was dubious as he smashed the bar when he should have squared to an unmarked Hwang Hee-chan.
The star, searching for his first goal of the season, then did an air-shot after the break. It let the Clarets off the hook as Wolves pressed in the second half for an opener.
But battling Burnley, who were without the suspended duo of James Tarkowski and Ashley Westwood, will feel they merited a point to make it just one defeat in eight games.
And arguably the best performer on the night was referee John Brooks, making his Premier League debut. He kept control of the game when other officials might have brandished a lot more cards.
Leander Dendoncker took until the 14th minute to test Burnley keeper Nick Pope with a header from Nelson Semedo's cross.
The visitors created some limited openings but Chris Wood miscued a header and showed few signs of adding to his five goals in three games against Wolves.
Proceedings livened up after Hee-Chan Hwang and Matt Lowton tangled and both went in the book.
Pope was soon tested again in the 25th minute as South Korea international Hwang fired in a left-foot effort.
Wolves were desperately unlucky not to take the lead in the 30th minute when Traore broke at pace.
But rather than opt to pick out the unmarked Jimenez, Traore unleashed a right-foot effort from the edge of the box which crashed back off the underside of the bar.
It didn't impress coach Bruno Lage on the touchline who clearly felt the Spain international should have passed.
And when the half-time whistle went, Wolves skipper Conor Coady walked off with his arm around Traore giving him advice.
Whatever Coady's tips, it didn't help the forward after the re-start when Rayan Ait-Nouri's cross fell for him but the star did an air-shot on his left-foot.
But Wolves remained the more dangerous side as Nathan Collins did superbly to crowd out Hwang when the ace threatened to turn and shoot.
As Wolves turned the screw and Lage tried to whip up the fans on the sidelines, Hwang and Traore had further efforts snuffed out by superb defending by Collins.
Traore said: "I think we are sad because we had a lot of chances to score. I was close to scoring but it was not enough.
"At the start of the season I had one v one situations. I have to score and that is why i work everyday. This is my main goal.
"We have to keep improving and working. We are having chances."
Clarets boss Sean Dyche added: "Defensively we were solid but we didn't deal with the ball well enough."