Pate, a tour rookie whose best finish was a tie for 10th at the Senior PGA Championship, carded a 7-under 65 to move into second place.
Andy Bean, who held the first round lead with Doyle and John Harris, posted a 2-under 70. He shares third place at 9-under-par 135 with Mark James, David Eger and Bob Gilder.
Doyle was steady to start the round with three straight pars. He picked up back-to-back birdies from the par-3 fourth and climbed to 10 under with a birdie at the seventh.
Doyle, an eight-time winner on the Champions Tour, notched his fourth birdie at No. 9, then posted three consecutive pars. He birdied the par-4 13th and picked up birdie No. 6 on the 15th at The National Golf Club of Kansas City.
The 55-year-old Doyle faltered to his first bogey of the tournament at the 17th, but came right back to birdie the last to grab a one-shot lead entering the final round.
'I played well again,' said Doyle, who has won four of nine events in which he held at least a share of the 36-hole lead. 'I drove it well and executed nearly every shot today. I got off to a good start today. Only bad hole was No. 17.'
Pate began his round on the back nine Saturday. He collected birdies at the 10th and 12th to get to 7 under. His next three birdies came on par-5s, Nos. 15, 18 and 5.
The 1976 U.S. Open winner drained his sixth birdie of the day at the seventh, his 16th. Pate then birdied the par-4 ninth to get within one stroke of the lead.
'I've been playing a lot better than my scores indicate,' Pate said. 'I played well for nine holes last week, but was 3 over on the back nine. It's been a long road coming back. It's been 15 years since I've played competitive golf.'
Harris managed a 1-under 71 to move to 8-under-par 136. Bruce Summerhays, a playoff winner here in 1997, is one stroke further back at minus-7 thanks to a second-round 65.
Dana Quigley and Jose Maria Canizares share ninth place at 6-under-par 138, with Gil Morgan, Lonnie Nielsen, Bruce Fleisher, Morris Hatalsky and 2002 champion Bruce Lietzke right behind them at minus-5.
Jay Sigel, the defending champion, stands at 1-under-par 143 after an even-par 72 in the second round.