As for Tottenham, Harry Kane and Dele Alli were both fit after recovering over the international break. Mousa Dembele, meanwhile, was preferred to Harry Winks in the middle of the park as Eric Dier dropped into centre-back.
A mistake from Dier presented Arsenal with the first half-chance of the match in the fifth minute, but Lacazette, having been found by Sanchez in a dangerous area, could only fire his effort into the stands.
It was the home side that were pressing forward in the early exchanges, with Lacazette, Alexis Sanchez and Ozil all causing problems to Tottenham's back three, which was without the influential Toby Alderweireld.
Lacazette had another opportunity in the 19th minute when Hector Bellerin delivered a terrific low cross into the Tottenham box, but the France international just could not make contact ahead of Dier and Davinson Sanchez.
Arsenal's pressure was still apparent as the first period approached its mid-point, with Lacazette a constant problem to Tottenham's back three. The Frenchman again came close to meeting a Sanchez pass just before the 30-minute mark, but Spurs goalkeeper Hugo Lloris was on hand to make the clearance.
Christian Eriksen hit a post for Tottenham in the 33rd minute after working space inside the Arsenal box, before Kane saw a header saved by Cech as the visitors had two good chances to make the breakthrough.
It was Arsenal that took the lead in the 36th minute, however, when Mustafi rose highest inside the Tottenham box to meet a floated free kick from Ozil. Spurs were unhappy about the awarding of the set piece though, with Davinson Sanchez appearing to cleanly win the ball against Alexis Sanchez in a wide area.
Arsenal then doubled their lead in the 41st minute when Alexis Sanchez smashed home after Lacazette had delivered a low cross into the Chilean, who put his contract issues aside with a fine performance.
Kane might have halved the deficit late in the first period after working space in the final third, but the striker sent his effort wide of the post as Arsenal entered the half-time break with a 2-0 advantage.
Tottenham had a couple of half-chances early in the second period, but Kane's header was comfortably collected by Cech, before Arsenal defender Nacho Monreal cleared a dangerous cross from Ben Davies.
Kane then had a strike blocked by Mustafi as the visitors looked to hit back before the hour mark at the Emirates.
Winks for Dembele was Tottenham's first change of the match in the 62nd minute, but Arsenal continued to have joy on the counter-attack as the Gunners looked to kill off the contest with a third goal.
Alexis Sanchez had two chances to score a third for Arsenal 20 minutes from time, but his first flew into the stands, before his second was comfortably collected by Lloris in the away side's goal.
Francis Coquelin for Lacazette was an indication of Arsene Wenger's thinking in the final 15 minutes of action, while Alli and Kane were replaced by Fernando Llorente and Son Heung-min for the visitors.
Cech flew across his goal to keep out a close-range Dier header 10 minutes from time, before Son fired over the crossbar in the 85th minute after Llorente had found his strike partner with a knockdown.
Tottenham continued to press, but Arsenal, who came close late on through Alexis Sanchez and Alex Iwobi, held firm to earn the North London bragging rights as they recorded their sixth straight Premier League home win of the 2017-18 campaign.