The leading trio was one shot clear of three Americans with 67s -- D.A. Points, Rick Price and Dave Schultz -- in the tournament co-sanctioned by the Australasian PGA and U.S. Nationwide tours.
Michael Campbell, the 2005 U.S. Open winner, shot a 70 and was among 49 players within four shots of the lead.
Hearn had six birdies and no bogeys and Stiles gave up the chance for the outright lead when he double-bogeyed the par-4 13th along with eight birdies.
Bettencourt held the lead at 7-under until he double-bogeyed the par-4 17th, then birdied 18 to reclaim his share of the lead.
Calm conditions and light drizzle favored low scoring in the morning but it was Hearn, Stiles and Bettencourt, among a group of players teeing off in the afternoon, who set the scoring pace for the day.
Stiles faltered only at the 13th which he had to play into a gusting wind.
'It's never a fun hole, especially when the breeze is blowing and coming in from the left. For me that's a tough wind anyway with the driver,' Stiles said. 'I didn't hit that bad of a tee shot but got a poor lie in the rough, hacked it up to the green and missed a 5-footer for bogey. But other than that, I'm really happy with how I played.'
Stiles underwent surgery in 1989 to remove a cancerous tumor from his jaw, has played periodically on the U.S. PGA TOUR but was forced to go through qualifying school this year to hold his Nationwide card.