England striker Jamie Vardy, who was heavily linked with Arsenal 12 months ago, scored a brace either side of a Danny Welbeck leveller that showed Arsenal's rearguard to be equally awful from open play and set-piece situations.
Lacazette is the seventh Arsenal player to score on his first Premier League appearance.
Olivier Giroud came off the bench to head a late victor after Aaron Ramsey had brought Arsenal level at 3-3 following a Jamie Vardy double for the visitors.
"I don't know whether it was a lack of concentration or just a lack of game management in the last ten minutes, but you then concede again from a set play in terms of being overpowered. I know how important he is not only as a player but also in the group".
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Giroud had been seriously considering his future following the £52 million club record signing of Alexandre Lacazette and Wenger's certainty but has been persuaded to stay in what is now a "super sub" role.
"It is fantastic", Wenger replied when asked about Giroud's willingness to fight for his place. "It was a relief for me he chose to stay". "Even when I played Giroud through the middle and him on the left he did very well on the left".
Despite only starting 17 games last season in all competitions, Giroud still scored 16 times - including an eye-catching scorpion-style kick against Crystal Palace.
"I love the man and the player", said Wenger.
It's likely no one is more relieved with the result than Arsenal manager Arsene Wenger, who kept his job after missing an invite to the Champions League for the first time in his 21-year tenure with the club and months of non-stop shouts of "WENGER OUT" from supporters.
"We went for a win and we deservedly earned it". "We let in some goals we could have avoided but we'll work to ensure we don't concede any more like that during the season".