Leandro Trossard and Martin Odegaard struck at the end of each half to take the Gunners one point clear of Manchester City, who have a game in hand.
Arsenal's season was in danger of coming completely off the rails after a three-game winless run.
Mikel Arteta's men lost in the Premier League for the first time in 2024 last weekend, 2-0 at home to Aston Villa, in between a Champions League quarter-final elimination by Bayern Munich.
However, they bounced back to keep the pressure on champions City, who beat Chelsea 1-0 to reach the FA Cup final earlier on Saturday.
"Massive win for us," said Arsenal captain Odegaard.
"It was a tough week for us, few tough results and emotionally really hard but we had to keep doing. Today was all about bouncing back and getting the win.
"Still a long way to go, still tight in the race, so today was all about getting back to business."
Arteta made just three changes from the side that lost 1-0 in Munich on Wednesday and it took some time for the sluggish visitors to find their stride.
Wolves boss Gary O'Neil claimed his side have been struck by the worst injury crisis he has encountered in his professional career.
Yet, the undermanned hosts were nearly in front when David Raya was forced to turn Joao Gomes' powerful effort onto the crossbar.
Arsenal had only fleetingly threatened before the break despite their dominance of possession.
But they got the slice of fortune they needed to kickstart their challenge for a first title in 20 years on 45 minutes when Trossard's mishit shot clipped in off the far post.
There was little in the way of goalmouth action in the second period as fatigue took hold of Arsenal in their fourth game in 11 days.
However, shorn of the threat of the injured Matheus Cunha and Pedro Neto, Wolves lacked the attacking inspiration to further dent their title aspirations.
Odegaard made the points safe five minutes into stoppage time by catching Jose Sa out at his near post.
Third-placed Liverpool can move level on points with Arsenal when they visit Fulham on Sunday.
Luton concede five
At the bottom of the table, Luton's hopes of survival were hammered by Brentford's 5-1 rout at Kenilworth Road.
Luton's heaviest home league defeat of the season leaves the Hatters still one point adrift of Nottingham Forest, who visit Everton on Sunday in a huge clash at the bottom of the table.
"Today was a bad day for us as a club but the teams directly above us play each other and we will not be out of it this weekend. It's important we all remember that," said Luton boss Rob Edwards.
Brentford realistically secured their top-flight status with a dominant display despite missing England striker Ivan Toney through injury.
Yoane Wissa struck twice before half-time, while Ethan Pinnock, Keane Lewis-Potter and Kevin Schade were also on target for the Bees.
Burnley are now within two points of Luton and three of survival after cruising to a 4-1 victory at rock bottom Sheffield United.
The Blades are destined to head straight back down to the Championship due to their woeful defending.
Jacob Bruun Larsen, Lorenz Assignon, Lyle Foster and Johann Gudmundsson were on target for Burnley to leave Chris Wilder's men 10 points adrift of safety with just five games remaining.
"I won't name names, but I think there were a few players out there who wanted to get out of there pretty quickly after the fourth went in," said Wilder. "You just can't have (that)."
