The French striker opened the scoring for Arsenal with a penalty, after Reece James brought Kieran Tierney down in the box. Xhaka then put Mikel Arteta's side two goals up before the break, with a sensational free-kick that gave Edouard Mendy no chance.
After half-time, Saka added to Chelsea's woes with what looked like a miscued cross that headed straight over Mendy's head and into the goal.
Tammy Abraham diverted a Callum Hudson-Odoi cross into the net and gave Chelsea hope, which turned into real optimism when they were given a late penalty for a foul by Pablo Mari. However, Bernd Leno saved Jorginho's spot kick to ease Arsenal nerves and win the three points for the Gunners.
Here's how each player fared at the Emirates Stadium tonight.
Arsenal Player Ratings
Bernd Leno - 7/10
Leno could do nothing to stop Abraham's goal. He guessed right and saved Jorginho's penalty well, and didn't really have much else to do.
Hector Bellerin - 7/10
Bellerin had a much better performance than the ones he put in before he was suspended. There was purpose to his drives forward, he showed quality with his passing, and defended well against Werner.
Rob Holding - 7/10
Holding made a few critical interventions in the box against the likes of Werner and Pulisic. He should have scored in the second half, but was denied by Mendy.
Pablo Mari - 7/10
In his first Premier League start of the season, Mari slotted in seamlessly in the Arsenal rearguard. He took the responsibility of dealing with the aerial threat of Abraham.
Kieran Tierney - 8/10
The Scottish left-back was outstanding, especially moving forward. He combined brilliantly with Martinelli, and played a critical role for the first goal by winning the penalty that Lacazette scored.
Mohamed Elneny - 6/10
Elneny brought energy and steel to the Arsenal midfield. However, he did sometimes play his team into trouble with some shoddy passing.
Granit Xhaka - 8/10
Much maligned in recent times, Xhaka produced a timely reminder of his quality. The free-kick was sensational, but his general play was filled with purpose and desire. His passing from midfield to the wide players was sublime as well.
Bukayo Saka - 8/10
Saka started on the right wing and tormented Ben Chilwell. He may or may not have meant the strike that got him his goal, but it was certainly a goal that his performance deserved.
Emile Smith Rowe - 7/10
For a young man coming into the first team in such a game, and in the situation that Arsenal are in, Smith Rowe was incredibly mature in midfield. There was control to his play in the No.10 role, and he linked up well with both Martinelli and Saka.
Gabriel Martinelli - 7/10
In their last two games, Arsenal have looked a different team with Martinelli on the pitch. The Brazilian's direct running caused Reece James all sorts of problems. He could've scored a worldie but didn't get enough power on an overhead kick.
Alexandre Lacazette - 8/10
This was Lacazette's best performance in a long time. His hold-up play was excellent, he linked really well with the other attacking players, and was strong while ensuring possession wasn't lost. He also tucked away his penalty easily.
Joe Willock - 7/10
Willock had a couple of chances immediately after coming on, but couldn't take either.
Nicolas Pepe - 6/10
He came on late in the game, and was a bit lazy at times, in not making the runs that he should have.
Shkodran Mustafi - N/A
Mustafi came on in second-half stoppage time, just to ensure that Arsenal had numbers at the back.