Triplett had a 69 at Del Monte to match Cochran at 9-under 135 in the tournament that features 81 players from the PGA, LPGA, Champions and Web.com tours.
John Mallinger, the 2010 winner, was a stroke back after a 69 at Spyglass Hill.
Triplett had one bogey and four birdies, including 15-footer on the ninth, his final hole of the round.
"I putted well and drove the ball into the fairway most of the day," said Triplett, who claimed his first Champions Tour title in July at Pebble Beach. "That's what you have to do at Del Monte to play well."
Cochran, the 2009 Champions Tour rookie of the year who had three top-10 finishes this season, had five birdies and began his round with an eagle on the par-5 first hole.
"I am very glad to be done," said Stallings, who won the True South Classic in Mississippi in July for his second PGA Tour victory. "I knew how to play the course, but the greens were super soft and mushy with the foot traffic. I had a few three-putts and short-sided myself a few times and wasn't able to get up and down."
Hall of Famer Annika Sorenstam was 5 under after a 69 at Spyglass.