The hosts squandered the first chance of the game after 10 minutes, as Nélson Semedo bombed down the wing before brilliantly crossing for Pablo Sarabia, who sliced his volley just off-target.
Arsenal’s best chances fell to Kai Havertz, as he flicked his first header marginally wide, and five minutes later, his second header was saved well from close range by José Sá’s outstretched leg – both from wonderful Leandro Trossard crosses.
However, just before HT, the visitors suffered a setback as Myles Lewis-Skelly was sent off for a foul on Matt Doherty.
Despite that, Arsenal started the second half the better side, as Declan Rice stung Sá’s palms with a powerful strike and it took an hour for Wolves to record their first shot on target, with Hwang Hee-chan testing David Raya from distance.
The hosts started to dominate from there with the extra man, as Raya was needed again to tip Arsenal-linked Matheus Cunha’s deflected effort away, before the Brazilian shot inches wide from the resulting corner.
However, a second red card levelled the playing field when João Gomes was shown a second yellow for a nasty challenge, allowing Arsenal capitalise four minutes later through substitute Riccardo Calafiori, who struck a half-volley that found its way into the bottom corner.
Wolves pushed for an equaliser late on as Rayan Aït-Nouri and Cunha both forced Raya into saves, but the Gunners held on for three precious points to keep them in the title race.
The Old Gold are now winless in five league matches, while the visitors keep a first clean sheet in 11 away league games.