Crawley bowed out of the EFL Cup at the first round stage but could consider themselves unlucky after an excellent performance at Molineux.
Reds recovered from the early loss of a goal by Joe Mason to equalise through a towering header by Enzio Boldewijn.
The hosts then had some excellent chances with Wolves keeper Andy Lonergan denying Adi Yussif while Boldewijn and James Collins went close to putting their side in front in the second half.
But it was the Championship hosts who won it with 15 minutes to go through Conor Coady’s close range header while Mason was denied a second by the post, although a two-goal margin of defeat would have been very harsh on the visitors.
Reds finished the game with ten men after Mark Connolly picked up yellow cards in the first and 89th minutes and will now miss Saturday’s League 2 trip to Doncaster Rovers.
Reds made one enforced change to the team that beat Wycombe on Saturday with Chris Arthur making his debut at left-back in place of the suspended Andre Blackman.
New Wolves boss Walter Zenga, who was in charge at Molineux for the first time, changed five players from the team which drew 2-2 at Rotherham in the Championship on the opening day.
Among the crowd was former Crawley boss Mark Yates and he saw the hosts go in front in the seventh minute, moments after Boldewijn had been denied by a goal-line clearance.
The Dutchman’s volley, after Connolly had headed down a corner by Jason Roberts, was athletically headed off the line by Conor Coady. Former Benfica midfielder Joao Teixeira led the counter-attack and when his angled effort came back off the far post, Mason was on hand to slide the ball into an empty net.
It was harsh on Reds who had made a decent start after Connolly had picked up a first minute booking for bringing down Mason but they responded superbly. Boldewijn and Young linked up on the right and Young’s cross was cleared for a corner from which Reds drew level on 11 minutes.
Roberts’ left-wing delivery picked out Boldewijn and he sent a flying header from close range soaring past the helpless Andy Lonergan to make it 1-1.
Reds had to make a 25th-minute change when Roberts failed to recover from an earlier knock and was replaced by Mansfield loanee Adi Yussif.
James Henry curled a free kick from a good position over Yusif Mersin’s goal and Baath headed a left-wing cross wide as Wolves, who were content to play out patiently from the back, tried to find a way through a compact Crawley who were working hard on and off the ball.
Reds should have gone in front on 38 minutes. James Collins’ pass picked out Yussif’s run perfectly but Lonergan did just enough to deflect the substitute’s right-foot shot wide of the post. Collins then tested the Wolves’ keeper with a low drive from distance as Reds continued to give as good as they got.
Kortney Hause lifted a stoppage-time free kick high into the Billy Wright Stand as the first half ended with Reds very much in the tie.
Wolves made a double change at the break with Helder Costa and Jon Dadi Bodvasrrson coming on and after Reds had defended a corner they had a chance of their own in the 48th minute when Yussif did well to cross from the left and Boldewijn’s header went just over. Moments later Hause almost cleared another Yussif cross into his own net then Jimmy Smith fired well over
inside a crowded box after Boldewijn had smuggled the ball into his path as Crawley continued to impress.
An hour into the contest and Reds continued to impress. Teixeira’s frustration boiled over when he was booked for simulation, his mood matched by the home fans as Crawley continued to look the side more likely to score.
They went close again in the 69th minute when Yussif’s pass played Collins in but his shot from a narrow angle rolled agonisingly wide of the far post. Reds then defended superbly with Joe McNerney blocking Costa’s shot before they were forced into a second change when early sub Yussif limped off and was replaced by Bobson Bawling.
Wolves began to up the tempo and thought they had regained the lead with 15 minutes left when Baath met Jack Price’s free kick but Connolly somehow got back on the line to head it away from danger.
But respite was short-lived. From another free-kick, this time by Teixeira on the left, Bodvarsson headed back across the face of goal and Coady’s diving header sneaked inside the post.
On the balance of play it was harsh on Crawley but Wolves pressed for a third and Teixeira saw his effort blocked for a corner by Connolly before Matt Harrold replaced Banton with nine minutes to go as Reds switched to 4-4-2 to try and get back into the tie.
Connolly had been on a disciplinary knife-edge after his early booking and with a minute of normal time to go he was sent off for his second booking, a foul on Costa.