Pate, the Turtle Bay Championship winner two weeks ago in Hawaii, had an 11-under 133 total on The Old Course at Broken Sound.
He eagled the par-4 13th, holing a sand wedge from 95 yards. The ball landed about a foot past the cup, jumped another 2 or 3 feet and spun back into the hole.
'That was exciting,' Pate said.
Hoch also shot a 67, birdieing four of the first seven holes.
John Cook (66), Bruce Lietzke (65), Mark McNulty (69) and Bobby Wadkins (68) were two shots back at 9 under, and defending champion Mark James (66) was 8 under along with Eduardo Romero (67), Jim Thorpe (67) and Ben Crenshaw (68).
'Tomorrow will be a nice opportunity to win,' Cook said. 'I think I'm hitting the ball as well as I ever have. I'm not hitting every shot great, but I'm hitting a lot of quality shots.'
Pate might be tough to catch.
'He's playing better than anyone else right now,' Lietzke said. 'He's on a roll, for sure.'
Hoch remembers watching Pate win two weeks ago in inclement conditions in Hawaii.
'If he can play that way tomorrow, it may be tough to catch him,' Hoch said. 'Luckily, we don't have a Tiger (Woods) out here.'
Saturday's round was played in ideal conditions, but the course was hit by a cloudburst with thunder and lightning just after the final putt was struck.
Cook believes it will take another round in the mid-60s to contend Sunday.
'But tomorrow's going to be completely different,' he said, referring to an expected change in wind direction.
He also said Pate will be hard to beat.
'He's looking like 1976 all over again,' said Cook, referring to the year Pate won the U.S. Open and Canadian Open.