UCF is in a tie for ninth heading into the third round. The top 8 teams after Thursday advance to match play on Friday.
Georgia Tech had its second straight 6-under 274 to reach 12 under on the Capital City Club's Crabapple Course. California was a stroke back, and defending champion Texas followed at 10 under. The top eight schools after the third round Thursday will advance to team match play.
Rahm had a 7-under 133 total for a one-stroke lead over Arkansas' Nicolas Echavarria and UCF's Greg Eason. Echavarria had a 64, and Eason shot 66.
Alabama was fourth in the team standings at 9 under, followed by Arkansas and Illinois at 3 under, first-round leader Arizona State at 2 under and Texas A&M at even par.
Ollie Schniederjans added a 68 for Georgia Tech, Seth Reeves shot 69, and Shun Yat Hak had a 70. Bo Andrews shot a 72 that didn't count in the team total.
Alabama was fourth in the team standings at 9 under, followed by Arkansas and Illinois at 3 under, first-round leader Arizona State at 2 under and Texas A&M at even par. Arizona State tumbled down the leaderboard with an 8-over 288.
Six schools were within four strokes of eighth place, including UCF at 1 over, and Oklahoma at 2 over.
Cal, which has won an NCAA-record 11 of 13 events this season, was 17 under at one point Wednesday, but the Bears' top four golfers played the last five holes in a combined 9 over. Georgia Tech's scoring players were even on those holes.
Yellow Jackets coach Bruce Heppler was content that his team -- with no players who have competed previously in an NCAA tournament -- didn't lose its composure as Cal was lighting up the scoreboard early.
"I'm hoping they're not looking because I can't go to zone instead of man-to-man, or a triangle-and-two," Heppler said. "You've just got to do what you've got to do. We can't control (Cal). They're a good team."
Rahm's second-round struggles left 14 players within three shots of the lead. Among those at 4 under was last year's medalist, Thomas Pieters of Illinois.
Cal senior Max Homa was 8 under after 15 holes, and Cal coach Steve Desimone said he thought his player might go as low as a 59. Instead, Homa ended up at 65 for a 5-under total.
As for his team, which won its only national title in 2004, Desimone said the Bears made things a lot tougher with their poor play at the end of the round.
"We were way up, and it looked like we were in really good shape," Desimone said. "It was party time. Now, it's root canal."
Homa bogeyed the 540-yard, par-4 16th into the wind and double-bogeyed 18, missing a 4-foot putt after lipping out from 40 feet.
"Sixteen is just a tough hole. I had a terrible drive. Even if you hit the fairway it's a pretty hard hole," he said. "I can't be too mad. It's going to happen. I'll take 5 under."