Marcos Alonso scored the decisive goal nine minutes from time as Chelsea shrugged off Arsenal's fightback to secure a 3-2 win at Stamford Bridge.
The full-back swept home Eden Hazard's cross to make it two wins from two under Maurizio Sarri and keep the Gunners waiting for their first Premier League point under Unai Emery.
It was a particularly galling end to the game for the visitors, who had dragged themselves level before the break thanks to Henrikh Mkhitaryan and Alex Iwobi, after Pedro and Alvaro Morata had put Chelsea two goals to the good.
Manchester City went ahead against the Gunners after 14 minutes last week, and Chelsea needed just nine to find the net, with Pedro finishing coolly from 12 yards after being teed up by Alonso.
It was 2-0 after 20 minutes when Morata turned away from Shkodran Mustafi and fired low past Petr Cech, just a minute after Pierre-Emerick Aubameyang, starting as the lone striker once more, had blazed over the crossbar with the goal gaping.
Mkhitaryan produced almost a carbon copy of Aubameyang's miss but made amends with a fine left-footed strike to get the away side back into the game, and Iwobi thumped high into the net from the Armenia winger's cross to level the scores before the break and leave the home crowd shell-shocked.
The Blues suddenly looked in disarray and could have been behind heading into half-time had Aubameyang and Iwobi been more accurate when finding space among a ragged Chelsea defence.
It was Sarri's men who looked the most likely to break the deadlock in a more scrappy second half, though, and they did just that with 81 minutes played, as Alonso finished with aplomb following fine work from substitute Hazard.
What does it mean: Gunners have more grit than first thought
It was nearly the first point on the board for Arsenal under Emery, but it at least showcased a quality they have been accused of lacking for several years now: character.
The Gunners truly looked dead and buried after half an hour but battled back into the game without resorting to a hasty abandoning of the passing style Emery is trying to implement. The defending, undoubtedly, still leaves much to be desired.
Mkhitaryan was at the heart of the initial comeback and it was a perplexing display from the ex-Manchester United star in general, as he recovered from a dismal first 35 minutes to haul his side back into the game almost on his own. That will be encouraging for a player who has never found consistency during his time in England.
For Chelsea, the result is a major boost given the way they surrendered their early control so readily. Sarri was calm and collected as the Chelsea goals went in, but was raging once Arsenal had drawn level, such was the ragged state of his side's defence.
His vision for the team is starting to appear, but it will take some time yet to come in to sharper focus.
Pat on the back: Mkhitaryan leads recovery
Mkhitaryan had a pretty dreadful first 35 minutes or so, summed up by his shocking miss from right in front of goal when Chelsea were in command.
However, the 29-year-old inspired the Gunners' comeback with an impressive improvement of his own. His fierce strike to get them back in the game was too hot for Kepa Arrizabalaga to handle and he picked out Iwobi with precision for a goal that looked likely to earn a point.
Boot up the backside: Aubameyang unconvincing
Aubameyang has said he likes Alexandre Lacazette partnering him in attack and, on this evidence, the Gabon striker certainly needs more support.
The Gunners' record signing managed only 18 touches in total, two of which included heart-stopping moments for the travelling fans: a decent finish from an offside position, and a miss that will grace highlights reels for the rest of the season.
What's next?
Chelsea head to Newcastle United next Sunday, the scene of a humbling 3-0 loss on the final day of last season. Rafael Benitez's side are still looking for their first victory this term.
Arsenal, having faced a daunting opening two weeks, will play host to a West Ham side who have lost two games out of two and conceded six goals in the process. That one takes place at Emirates Stadium next Saturday.
