Price and Montgomerie shot 67s at Prestonwood Country Club in the 50-and-over tour's regular-season finale. Kelly birdied four of his last six holes to shoot 68 and join them atop the leaderboard.
Both Price and Montgomerie seem to be in good shape in the chase for the tour's playoffs, with Montgomerie entering in seventh place in the Charles Schwab Cup standings and Price at No. 33. The top 72 will advance to the playoff opener next week in Richmond, Virginia.
Montgomerie said he places a high value on playing well entering the playoffs, especially after injuries caused him to start the season slowly, and joked that the goal for him and everybody else on tour is to catch money leader Bernhard Langer.
The 60-year-old German star, who won this tournament in 2012, is coming off his fifth victory of the season three weeks ago at Pebble Beach and is seeking his ninth money title in 10 seasons. Langer shot 68 on Saturday and is four shots off the lead.
"A few guys are getting tired, and hopefully I can just push on," Montgomerie said. "Obviously we're all trying to catch the German, you know? That's what we're doing the last bloody three years, and let's hope somebody can do it this time, but he's the standard and all credit to him."
Price made a late move up the leaderboard, with four birdies in the five-hole span of Nos. 13-17. The 50-year-old from Wales, in his first year on the PGA Tour Champions, is trying to secure his card for next year.
"I need some great weeks," he said. "I've got so far to go, I just need to play well at the end and hope I sneak in."