Allen, the 2009 Senior PGA Championship winner, had nine birdies in his bogey-free round at The Woodlands Country Club. Cook, the 2008 champion and a three-time winner this year, also had a bogey-free round.
'I don't think you ever think you'll go out and shoot 63 – 9 under,' Allen said. 'I was in a good frame of mind, just playing the shots.
'Overall, it's been a fairly consistent year,' Allen said. 'It's been a little frustrating that I haven't won. My main goal, I wanted to come out here and play two weeks in Texas and see if I can get this first win under my belt. I'd like to get out with another one of these and bury these guys. We'll see what happens.'
Allen began play on No. 10, and made birdie putts of 12 feet on No. 11, 20 feet on No. 13 and 12 feet on No. 15. He took the lead for good when he hit a 4-iron to 3 feet to set up a birdie on No. 6 that got him to 8 under. He holed a 12-foot birdie putt on the final hole to extend the lead.
Two-time winner Bernhard Langer was 7 under after 16 holes, but hit into the water on No. 17 en route to a double bogey and followed that with another double bogey on 18 for a 69.
The German star won the 2007 event at Augusta Pines and successfully defended his title in 2008 at The Woodlands. He shot a tournament-record 62 in the opening round of his 2007 victory.
Couples opened with an eagle on the par-5 first and was 4 under after 12 holes. He made a double bogey on the par-5 15th, then birdied Nos. 16 and 17.
Lehman, a three-time winner this year, has a 398-point lead over Calcavecchia in the Schwab Cup standings with three events left.
Allen was two strokes off the best round of his Champions Tour career, a 61 in the third round of the 2010 Schwab Cup Championship. 'I just kind of played the shots I had,' Allen said. 'I was obviously playing them quite well and when I got the 10-footers I was making them with no problem today. That was nice. I don't think I did anything I don't always try to do.'