McGovern birdied three of his last four for a 3-under 68, while Points posted two eagles and four birdies for an impressive round of 8-under-par 63 on Saturday.
The pair is knotted at 17-under-par 196, which matched the 54-hole tournament record. Rick Cramer established the mark in 1996 and Mario Tiziani matched it last year.
Aron Price carded a 6-under 65 on Saturday and is tied for third place with Brenden Pappas, who shot a 3-under 68 in round three. They are knotted at minus-15.
McGovern rolled in a 40-foot birdie putt at the fifth, but fell behind due to Points. At the par-4 12th, McGovern missed the green with his approach and chipped 12 feet past the hole. He missed the putt for his first bogey of the week, but his finish would get back to the top of the leaderboard.
At the 15th, McGovern's approach bounced off the green, but he putted it in for a birdie. He added birdies at 16 and 18 to join Points in a tie for first place.
McGovern will be in search of his fourth Nationwide Tour win. All of his victories on this circuit came in 1990 when it was called the Ben Hogan Tour. McGovern won the 1993 Houston Open on the PGA TOUR.
Points made it clear from the beginning he was making a charge. He eagled both the second and third, both par fives, then caught fire again around the turn.
At the ninth, Points ran home a 15-foot birdie putt to tie McGovern at 14-under par. He sank a 25-footer for birdie at the 10th, then converted a 7-footer at the 11th for his third birdie in a row.
He parred his next five holes, but Points hit his tee ball nine feet from the hole at the par-3 17th. He drained the birdie putt and parred the 18th to put himself in position for his fourth Nationwide Tour victory and first since 2004.
'I played really solid the entire day,' said Points, who only took 24 putts on Saturday. 'I had a lot of looks. It was really an easy, fun day. It was one of those days.'
Peter Tomasulo (64), Boyd Summerhays (65), Matthew Jones (67), Jon Mills (66) and Todd Demsey (68) are tied for fifth place at 14-under-par 199.
Brock Mackenzie (65) and Garth Mulroy (68) share 10th at minus-13.