The visitors saw goals from Helder Costa and Diogo Jota chalked off for offside, while the latter was guilty of spurning a golden opportunity when he skied over from only a few yards out.
For the most part, both teams were restricted to attempts from outside the box but Jota also rattled the bar in the second half for Wolves, while George Moncur fired a great chance wide for Barnsley in the final 10 minutes.
However, Barnsley head coach Heckingbottom felt a share of the spoils was a fair result.
Sheffield sexual assault: Girl, 13, victim of 'serious' sexual assault in Chapeltown
Caught on camera in Sheffield: 10 people police want to speak to in connection with criminal investigations
RSPCA: 9 cats and dogs looking for a new home this month at Sheffield's RSPCA branch
Chesterfield Road Sheffield: Man arrested on suspicion of threats to kill after being brought down from roof
Adult social care Sheffield: Anger as council fails to pay costs as couple’s savings dwindle away
He said: "It's a good point. For a 0-0 we saw limited goalmouth action - I enjoyed it. It was high-intensity, competitive and good football.
"Both teams were good at defending, organisation and discipline.
"It's difficult. We saw when we played Wolves away how good they are defensively.
"They are the best team defensively in the league and from set plays. We still struggle to create chances against them because they are a good side.
"If they get in front they're a different team. Neither team did enough to win it.
"All the players have had a chance and it's up to them to stay in the team. Whoever performs well enough deserves to be in the team.
"That's the fourth clean sheet in six or seven and we've been really competitive. That's the type of performance we expect to deliver.
"We've got a young side - we've got a side jumping up a lot of levels."
Wolves' lead at the top of the second tier standings was cut to 10 points but boss Nuno Espirito Santo was content to come away from Yorkshire with a draw.
He said: "This is football, it's a tough game. Barnsley fight, they are well organised, they have a game which is difficult to break.
"If there was going to be a winner it would be Wolves. We didn't concede anything to Barnsley.
"Teams are trying to adapt their shape to our idea. That was not the case of Barnsley. Paul knows what he's doing. There are a lot of teams adapting but that makes you grow.
"It's a challenge knowing that you have to find solutions - grow and play better.
"We are fighting from day one for every single point. There is not one day where we don't work hard.
"The work of Leo (Bonatini) was fantastic. He drops and plays, he supports. The goal will come for Leo, it will come naturally."