The 26-year-old, who moved from Olympique Lyonnais this month for a fee British media put at 46.5 million pounds, paid an almost immediate dividend on his five-year deal at Sydney's Olympic Stadium.
Lacazette came on for his Arsenal debut as part of a 10-man substitution in the 68th minute and was on hand 15 minutes later to sidefoot the ball into the net from winger Alex Iwobi's cutback.
"It is important for him to get that off his shoulders because you expect to score if you are a striker," manager Arsene Wenger told reporters.
"You could see that he was happy but overall what we were looking for was to play at pace and to develop our collective game and for long periods in the game that was quite good for us."
Arsenal, who also play Western Sydney Wanderers on Saturday before heading north to China, had taken an early lead when captain Per Mertesacker took advantage of some hesitancy in the Sydney FC defence to score with an overhead kick.
The Australian champions had goalkeeper Andrew Redmayneto thank for not succumbing to a heavier defeat as the 28-year-old, who had a two-week trial at Arsenal as a youngster, pulled off a string of fine saves.
"We had tough opposition because they fought for every ball but at the end of the day their goalkeeper was the man of the match," Wenger added.
One of Redmayne's saves was of a Danny Welbeck penalty but Wenger was overall pleased with the England striker's work-rate.
"I would say that he worked very hard," Wenger said. "He made many chances in the first half and was so keen to score that sometimes he looked too much for power.
"He put into the game what we expect of him. He’s a great team player and I expect him to have big season. He was out for such a long time that I hope this will be a positive season for him."
Arsenal's other French striker, Olivier Giroud, also came on in the mass substitution despite speculation over his future with the North London club.
(Reporting by Nick Mulvenney, editing by Greg Stutchbury)
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