The savvy 55-year-old golfer got off to a rocky start with bogies on the first two holes.
He then birdied nine of the remaining 16 holes en route to a 5-under-par 66.
“It feels really good considering we are playing against a bunch of college kids,” Greer said after his round.
“Despite a couple three-putts, I feel that I rolled the ball well today. This course is in excellent condition.”
Birdies on holes 5, 6 and 8 helped secure a 1-under par 34 on the front side.
In addition to the final three holes, Greer made birdies on holes 11, 12 and 14 on his way to a 4-under par 32 on the back nine.
Alabama’s Trey Mullinax, last year’s invitational champion, finished seven strokes behind Greer and out of the top 10 Friday.
Four golfers are only one shot behind Greer, including Bob Cox, Bobby Spiller, John Michael O’Toole and Matt Gourgeot.
Greer realizes anything can happen in the final two rounds of the mid-summer tournament.
“I have to keep making birdies and pars,” he said.
“I have to stay out of my own way.”