The Gunners headed into the game on the back of a 2-2 draw against Aston Villa at the weekend, having surrendered a two-goal lead.
However, they were able to put the draw behind them and got a 1-0 victory over struggling Wolves.
As it happened
The Wolves team were unchanged from their 3-1 defeat at Chelsea on Monday, while Mikel Arteta made five changes from Arsenal's 3-0 Champions League win over Dinamo Zagreb in mid-week.
William Saliba and Ethan Nwaneri returned for the Gunner, with Martin Odegaard and Mikel Merino missing from the squad.
Arsenal started the game brightly but could not get the lead in the first half instead got a red card via a Lewis-Skelly tackle.
In the second half, Arsenal showed more intensity despite being one man down and pushed the hosts back to their half.
As the game went on, Wolves also got a man sent off, which puts the game back into balance for Arsenal.
Shortly after the red card, Arteta’s men took the lead through substitute Calafiori. The Gunners held on until the final whistle and claimed a narrow win over Wolves.