Bukayo Saka scored with a fantastic finish 10 minutes before half-time, and Mikel Arteta's side held on despite multiple Leeds chances in the second half in an ultimately uninspiring performance by the league leaders.
"My heart is still racing but I'm just really happy to get the three points," Saka told Sky Sports. "It was a really tough game. Leeds did well, especially in the second half, and they put a lot of pressure on us.
"Big momentum for us, we've won another game. We need to keep this going and today we showed we can win no matter what."
Play was suspended for 40 minutes immediately after kick-off due to a VAR power outage. Sources told ESPN the hawkeye van had a power outage, meaning there was no communication between VAR and officials.
Both sides had chances in the first half but it was Arsenal who opened the scoring through Saka after 35 minutes.
Arsenal struggled to impart their usual passing game in the second half due to Leeds' insistent pressing -- twice Arteta's side were nearly punished for slack passes in defence shortly after the break.
Jesse Marsch's side had the better of the Premier League leaders in the second half and their good play looked to finally reap reward when they were awarded a penalty an hour in after William Saliba was penalised for a handball.
Bamford, though, dragged the effort wide of the right post with Aaron Ramsdale diving the right way as Arsenal's poor second half continued to go unpunished.
Ramsdale was again forced into action as he acrobatically palmed away Brenden Aaronson's long-range strike.
And after relentless probing, Leeds managed to force late drama and thought they had another penalty.
Bamford charged into Gabriel who fell and kicked out at the Leeds forward, giving the hosts a stoppage-time penalty with a red card being dealt to the Arsenal defender. However, after consulting VAR, referee Chris Kavanagh changed his decision and brandished a yellow card to Gabriel, while also rescinding the penalty decision -- allowing Arsenal to see out their narrow win.
"It was a really good performance from us. Discipline, concentration over the entire match even with the late start," Marsch said.
"A performance that showed that when we play the way we want to play, we can be very good. That's the best team in the league right now and today we were better."