Goals by Jelle Vossen and Patrick Bamford gave the Teessiders three crucial points, but wins elsewhere for Bournemouth and Norwich meant Middlesbrough remain third in the race for the Premier League.
Wolves hit back through Bakary Sako and then pressured for a leveller, with Rajiv van La Parra hitting the bar, with Boro grinding out a hard-fought win.
Boro were on fire in the early stages and opened the scoring in the third minute when Adam Clayton lumped the ball to Bamford and the Chelsea loanee selflessly pulled back for Vossen, who side-footed past Carl Ikeme.
It was Bamford’s 17th league goal of the season – beating Fabrizio Ravanelli’s 18-year Riverside record.
Wolves looked for an instant response when they won a free-kick near the edge of the area, but Sako’s effort was well over.
And it was rampant Boro who found the net again after 11 minutes. Czech full-back Tomas Kalas ghosted into the right side of the box before squarring for Bamford.
The forward’s first touch was not great, but he made amends when he turned and volleyed past Ikeme.
The visitors refused to lie down, though, and went close to reducing the arrears soon after Boro’s second, but Van La Parra’s shot was deflected over the bar.
Winger Albert Adomah was inches away from bagging Boro’s third when his mazy run ended with a thumping shot which came back off Ikeme’s crossbar.
The home side went close again after 50 minutes when Kalas raced down the right wing and hit a strong cross into the box for Vossen but his volley flew over the bar.
But Wolves pulled a goal back three minutes later when Edwards picked out Sako with a long ball across field, and the Mali international broke into the box before thumping a left-footed effort past Dimi Konstantopoulos.
Boro pressed for a third and they forced a free-kick 20 yards from goal but Lee Tomlin’s set-piece was easily cleared by the visitors.
Wolves should have levelled midway through the second half when substitute Scott Golbourne picked out Van La Parra in oceans of space at the back post, but his first-time effort rattled the bar and it was a let-off for Boro.
Tomlin showed great skill in the 85th minute when skipped past Danny Batth and hit a 20-yard drive which flashed past Ikeme’s post.
Bamford almost bagged his 18th goal of the season in stoppage time when he was put clear but his clever lob just clipped the crossbar.