The round was suspended due to darkness after the start of the round was delayed for just over an hour due to frost on the Crenshaw Cliffside Course at Barton Creek Resort. There were 42 players left on the course when play was called for the night.
Matt Hansen and Omar Uresti share second place at 7-under-par 63. Matt Bettencourt was one stroke further back at minus-6.
Gillespie got off to a slow start with six consecutive pars. He then dropped in back-to-back birdies from the seventh to make the turn at minus-2.
On the back nine, the 26-year-old turned it on. Gillespie birdied 10 and 12 to climb the leaderboard. He again made consecutive birdies from the 14th.
Gillespie, a two-time winner on the Canadian Tour, drained an eagle putt from 25 feet out at the par-5 16th to jump to minus-8.
The Ontario native got a good bounce out of the rough on 17 as his tee shot came to rest 4 feet from the hole. He sank that birdie putt and converted another 4-footer for birdie at the last to set a new course record by two strokes.
'That was just crazy,' Gillespie said. 'Even early on, I hit some great shots and gave myself some chances, but couldn't make a couple of putts. Things just went my way today, and it's not often you can say that.'
Ben Bunny and Brian Guetz were tied for fifth place at 5-under-par 65.
Paul Danielson, Rob McMillan, Jason Schultz, Karl Diewock, Ryan Ellis, Robert Hamilton and David Mathis completed their rounds at minus-4. They were joined there by Kyle Monfort, who has played 12 holes of his opening round.