Cardiff twice came from behind to level the scores, but Lacazette's 81st-minute strike proved enough for the Gunners to collect all three points from Wales.
Cardiff's high press made it an uncomfortable start for Petr Cech between the Arsenal sticks, with the experienced goalkeeper almost caught out on a couple of occasions inside his own box.
Cardiff had a golden chance to take the lead in the eighth minute when Cech presented Harry Arter with the ball in a shooting position, but the midfielder's strike was too high.
Granit Xhaka sent a long-range effort wide of the Cardiff post as the match approached the 30-minute mark, before Reid saw his over-head kick fly over the crossbar down the other end of the field.
Arsenal almost doubled their lead in the 33rd minute when Lacazette looked to pick out the bottom corner with a low strike, but the ball rebounded off the inside of the post.
Cardiff another super chance late in the first when a header from Sean Morrison fell for Arter in a dangerous position, but the on-loan Bournemouth midfielder sent the ball into the stands.
More suspect passing from Cech presented Cardiff with the chance to take the lead early in the second period, but Hoilett's effort was wide of the post.
Lacazette had Arsenal's first chance of the second half in the 50th minute, although the Frenchman's effort from close range flew high of the Cardiff goal.
Mustafi then saw a close-range header saved by Etheridge, before Xhaka's powerful strike deflected wide of the post during an eventful period of the match.
Arsenal did eventually regain the lead in the 62nd minute when Pierre-Emerick Aubameyang completed an excellent passing move by firing the ball into the bottom corner of the net.
Cardiff again came from behind to level in the 70th minute, however, with Danny Ward angling a brilliant header into the bottom corner after Morrison had made first contact.
Etheridge then kept out another Mustafi header 15 minutes from time as Arsenal looked for a third, with a low cross from Bellerin almost falling for Ramsey during an open spell.
Cardiff were having their moments, however, and Reid tested Cech with a strike in the 79th minute.
Arsenal took the lead for a third time in the 82nd minute though, with Lacazette firing into the top corner after turning inside the Cardiff box once again, and that proved to be the winner at the Cardiff City Stadium.
The home side did have a golden chance to level in stoppage time when Kenneth Zohore found the head of Morrison, but the centre-back headed over the crossbar.
CARDIFF (4-3-3): Etheridge; Manga, Morrison, Bamba, Bennett; Arter, Camarasa (Madine 89'), Ralls; Reid, Ward (Zohore 84'), Hoilett
ARSENAL (4-3-3): Cech; Bellerin, Mustafi, Sokratis, Monreal; Xhaka, Guendouzi (Torreira 70'), Ramsey; Ozil (Welbeck 84'), Aubameyang (Mkhitaryan 89'), Lacazette