Callum Robinson had Simon Grayson's charges dreaming of an upset with his seventh-minute goal at Deepdale, only to see Aaron Ramsey level a minute into the second half ahead of Giroud's 89th-minute winner.
The Frenchman, who has been a peripheral figure for much of the season, has been the Gunners' savour in recent weeks, with this goal following a late equaliser at Bournemouth and a late winner against West Brom.
He also scored a first-half goal in the 2-0 win over Crystal Palace in what was just his second Premier League start of the season.
After the Preston win, a delighted Wenger saluted Giroud, who was made captain for the clash.
The manager said: “He has scored many goals recently. Everybody contributes and he's in good form at the moment. It's been goal after goal.
“I like to rotate the captaincy. He went through a period of discomfort when he didn't play and that was quite long but he kept his focus and worked. He's shown leadership qualities and that's why he was captain.”
Preston were unfortunate not to build on their first-half efforts as Arsenal hit back after the break, with Wenger impressed by their efforts.
He added: “Preston had chances and we were just not at the pace the game demanded. Preston were organised and were quick in the transition. We were in trouble every time.
“They played in a very intelligent way. They are a good side, I was really impressed.”