The American carded a seven under 63 around a benign Hurstbourne Country Club, enough to finish tied the top of the leaderboard with Steven Fisk, Troy Merritt and Germany's Stephan Jaeger.
Two sharp shots - an 11-footer for birdie on the 17th and a 163-yard iron to three feet on the last - buoyed Glover.
"Very similar to last week, the first couple days, hit it nice, made some putts and no bogeys," said the 46-year-old, who also opened with a 63 at the John Deere Classic last week.
"Always a good way to start, First time here at this course. Absolutely love it. Wish we played more like it."
Sweden's Pontus Nyholm and Chan Kim were one shot back. Nyholm enjoyed the easy scoring conditions.
"It was pretty easy this morning - no wind and pretty soft greens," he said.
"The course is challenging in itself, but I felt like sort of the hardest part about this course is when it gets firm, just the angles get super important."
Max Homa - who finished second last week at the John Deere Classic - opened with a 67, four shots off the pace.