The tournament has 16 two-player teams from the PGA Tour and the LPGA, the second year of the mixed-team format.
The Canadian duo of Brooke Henderson and Corey Conners had two late eagles and narrowly missed a birdie on the 18th hole at Tiburon Golf Club.
They had to settle for a 59, tied with Akshay Bhatia and Jennifer Kupcho.
UCLA alums Knapp and Tavatanakit have a natural connection having played for the UCLA Bruins a few years apart. Their team name is "Rocco" - Knapp briefly worked as a bouncer before joining the PGA Tour and Rocco's Tavern is a popular spot in Westwood for students.
"Really chill," Tavatanakit said in describing the day. "I feel like everything was going the way we hoped for. The timing, momentum-building moments were pretty good. We just kept on playing."
They cooled slightly after opening with nine birdies. Knapp hit a towering shot into about five feet on the par-5 17th to set up eagle, and Tavatanakit poured in a birdie putt from about 15 feet on the 18th for the lead.
"I knew nine under wasn't going to be a bad score after nine holes," Knapp said. "But a couple of pars to start off the back nine it was like, 'OK, let's make sure we try to keep giving ourselves opportunities.' And to be able to finish eagle-birdie, that's always pretty nice."
Knapp won his first PGA Tour title at the Mexico Open. Tavatanakit won her first major as a rookie, the ANA Inspiration.
Maja Stark and J.T. Poston had a 61 and were joined by Sahith Theegala and Allisen Corpuz.
Defending champions Lydia Ko and Jason Day were at 62 with Jeeno Thitikul and Tom Kim.
Ko and Australian Day were slowed by a bogey on the third hole, rare for the scramble format.
Thitikul last month won the CME Group Tour Championship at Tiburon and the $4 million prize, the richest in women's golf.
The format changes to foursomes on Saturday, the toughest of the formats because one golf ball is in play and the teammates alternate hitting shots.
