At one point three ahead of the chasing pack, former U.S. Open champion Glover bogeyed the 14th and 17th in breezy conditions before signing off in style with a two-putt birdie at the par-five last.
In pursuit of his first PGA Tour victory in nearly two years, the 33-year-old carded a two-under-par 70 to post a 14-under total of 202 at the TPC Louisiana.
"The wind picked up a little bit more than was forecast," Glover told Golf Channel about the tougher conditions facing the late starters on a mainly overcast afternoon. "There was a bunch of good scores earlier and we knew that.
"I knew there were some birdies there, I just didn't take as much of an advantage as I should have."
Fellow Americans Kyle Stanley (65), Jimmy Walker (66), Billy Horschel (66) and D.A. Points (70) were tied for second at 12 under with burly compatriot Kevin Stadler a further stroke back after matching the day's best score with a nine-birdie 65.
British world number four Justin Rose, the highest-ranked player in the field, was five off the pace after returning a 70 with defending champion Jason Dufner a further shot back at eight under, after a 67.
Twenty-eight players are within six strokes of the lead heading into Sunday's final round but Glover, who clinched his only major title at the 2009 U.S. Open, remains in command.
"Tee to green is pretty good, although today wasn't as good as the first two days, and my irons were okay," Glover said of his overall game. "I hit some loose shots today.
"I had a few mis-reads and my (putting) speed was a little off today. I left a bunch of 10, 12-footers short."
While Glover was delighted to be contending for first PGA Tour title since the 2011 Wells Fargo Championship, he and his wife Krista are excitedly expecting their first child.
"Any day now," he smiled. "I don't care when the phone rings, I will be out of here for that. We're at 37 weeks and I can't wait. We are thrilled."
One stroke ahead overnight, Glover doubled his lead with a birdie at the par-five second where he got up and down from an awkward lie in a greenside bunker, splashing out to inside two feet.
Though Glover faltered with a bogey at the fifth after missing the fairway to the right off the tee, he regained a two-stroke cushion with a two-putt birdie at the par-five seventh.
Glover also birdied the eighth, after hitting a superb approach to nine feet and sinking the putt, before reaching the turn two ahead at 14 under.
Another birdie followed at the par-five 11th, where he sank a six-footer to stretch his lead to three, but he surprisingly bogeyed the par-three 14th after pitching to inside three feet from just off the green before missing the putt.
Glover did well to save par at the 16th where he missed the fairway to the left despite taking an iron off the tee but bogeyed the par-three 17th after lipping out with a seven-footer.
After splitting the fairway off the tee at the par-five 18th, Glover struck a stunning five-wood 268 yards from a downhill lie to 12 feet, then coolly two-putted for birdie.
China's 14-year-old Guan Tianlang, who once again stunned the golfing world by making his second consecutive cut on the PGA Tour this week, battled to a five-over 77 to finish at two-over 218, stone last in the 71-strong field.
"I just didn't do very good in the morning and was definitely in trouble with my driver," Guan said after mixing three birdies with five bogeys and an ugly triple at the sixth.
"I played pretty good in the middle of the round but still it was not a very good round for me."
Due to the threat of afternoon thunderstorms forecast for Sunday, tee times for the final round have been brought forward with the start scheduled from 7 a.m. local time (1200 GMT).
- Sports & Recreation
- PGA Tour