Manager Mikel Arteta remains unbeaten in all of Arsenal's Premier League visits to Stamford Bridge since he took the reins in December 2019, as his side left with all three points in a game of few clear-cut chances.
The central defender poked a probing goalward-bound looped effort from Bukayo Saka over the line for the only goal of the game in the 63rd minute.
Chelsea had been looking to return to winning ways in the league having been hammered 4-1 at Brighton the previous weekend, with manager Graham Potter suffering his first defeat since he took charge of the club in September.
However, the Blues struggled to impose themselves on the game, and finished with just two shots on target.
Chelsea's Kai Havertz had the best of the early chances inside the first 10 minutes. After being played in down the left at the edge of the box, he managed to get a shot away, but it did not trouble Aaron Ramsdale in the Arsenal goal.
The Gunners had an opportunity of their own in the 18th minute when Gabriel Martinelli tried his luck from range, but it flew over the bar.
Another chance fell the way of the visitors when Martinelli tried to pick out Gabriel Jesus at the far post, but the Arsenal forward was unable to direct his header from point-blank range goalwards.
Pierre-Emerick Aubameyang, facing his former club for the first time since leaving the Gunners by mutual consent in February, was routinely booed and jeered by the travelling support.
After a quiet first half, he had a half-chance at the start of the second, but his attempted strike was blocked.
Arsenal had looked the more likely to break the deadlock, but they did not have a shot on target until Gabriel made the decisive breakthrough.
Saka's corner was not dealt with by the Chelsea defence, and it looked on course to be already heading for the back of the net, but Gabriel made sure.
Following the goal, Arsenal looked the most likely to find the net for a second time.
Martin Odegaard missed an opportunity to add to Arsenal's tally when he was played in expertly by Jesus on a quick counter-attack. The Norway international had time to take a touch and create space to shoot from the edge of the box, but his effort sailed over the bar.
Going behind sparked a bit more from Chelsea, as they looked to attack on the break, with Ben White having to get to the ball ahead of the Blues forward line, and Gabriel also hooking the ball clear in the final 10 minutes.
However, the home side did not significantly test Ramsdale in rainy conditions in south-west London.
In stoppage time, Granit Xhaka squared up with Trevoh Chalobah, but referee Michael Oliver did not show any cards for the altercation in front of the Arsenal fans.