Tommy Fleetwood, who leads the Race to Dubai ahead of Garcia and Rahm, had some ground to make up after a par 71.
Molinari chipped in for birdie at No. 18, his ninth hole of the day, and finished with nine birdies and two bogeys.
''I started pretty much where I left off last year,'' Molinari said.
With no ticket fees, Molinari had a lot of fan support.
''It's great to see the crowds,'' he said. ''I think there's a nice buzz around the place and I'm happy and proud to be part of it.''
Thailand's Aphibarnrat led for most of the morning after sinking four birdies in his first eight holes before saving par at the 18th.
''This course really suits my game - small greens, quite a narrow golf course - and my driver and putter are working so well,'' Aphibarnat said.