The 39-year-old stormed to the turn in three-under-par 33 to sit second on his own at one stage.
He then started for home by dropping three shots in a row but rallied to card a one-under-par 71.
It left him sitting just outside the top 10 and only three shots off the lead, held by American Bill Haas.
“I’d say one-under was just,” declared Gallacher, who birdied the second, sixth, ninth and 15th. “It would have been a bit harsh if I’d had to settle for level-par.
“It’s a good start to the week and hopefully I can build on it. I hit one poor shot by going through the fairway at the tenth.
“Apart from that, I never really hit a poor shot and it was a solid round.
“I was on both the eighth and 13th in two and, while I didn’t make birdies at either, it was down to having tricky putts.”
He wasn’t alone among the record number of rookies in the field to make a promising start, with FedEx Cup leader Jimmy Walker, fellow American Kevin Stadler and Swede Jonas Blixt all signing for 70s.
“I think there are so many first-timers in the top ten at the moment due to the fact they don’t have any bad memories,” observed the Scot.