The reigning Olympic champions were only fourth fastest in the qualifying round, behind Australia, Britain and Denmark.
Riding their eye-catching 3D-printed Pinarello track bikes, the Italians certainly looked the part but the quartet of Ganna, Simone Consonni, Francesco Lamon and Jonathan Milan shed time late on in the 16-lap event.
Australia, bidding to win the men's team pursuit gold for the first time since Athens 2004, clocked 3:42.958 at a sweltering National Velodrome with Italy's time 3:44.351.
Tuesday's first-round heats pitch Italy against Australia with the losers out of gold medal contention.
"You never know what Italy are going to pull out in the next couple of days, but we are very proud of what we have done so far," Australia's Kelland O'Brien told reporters.
His teammate Sam Welsford said there was still more in the tank as they looked ahead to riding off against Italy.
"We nailed the process and the preparation. It has been a huge focus here," he said.
"We had a lot more to give at the end of that race."
Italy's Milan, part of the team that won gold in Tokyo, suggested that the champions were not yet at full throttle.
"It's pretty good. We are quite satisfied. We know we had some pretty tough competitors and we have marginal gains to play," he said. "We didn't go flat out, not really.
"We have to be a bit careful. I'm pretty positive. Now we have to rest as much as possible and come back tomorrow (Tuesday) as fresh as we can."
Tuesday's heats see New Zealand face Belgium, France against Canada, Britain against Denmark and Australia versus Italy.
The two fastest winners contest the gold medal race on Wednesday while the two slowest winners meet for bronze.
