Allenby picked up a quick birdie at the par-3 second and played his second shot to 3 feet for a birdie at the par-4 third. At the par-4 fifth, Allenby hit a wedge to 8 feet and converted the birdie try to reach 6 under.
The Australian added a birdie at the par-5 sixth, but he gave that shot back with a bogey at the par-5 ninth. Allenby recovered at the par-4 11th and dropped a wedge inside 6 feet for a birdie.
Allenby hit an 8-iron inside 10 feet for a birdie at the par-4 14th to move to minus-8. He continued his fine play down the stretch and drained another 10-foot putt for a birdie at the par-4 16th.
'I haven't been hitting the ball that bad, but I just haven't been putting or chipping very well,' said Allenby, who has experience inflammation in his hands this season. 'After the U.S. Open, I'm going to do an allergy test. So hopefully I'll get to the bottom of it soon.'
Scott knocked his second shot within 6 feet for a birdie at the par-4 first, but he found trouble with a bogey at the very next hole. Scott responded with a birdie at the third and rolled in a 15-foot putt for a birdie at the par-4 fifth.
At the par-5 ninth, Scott hit a wedge inside 5 feet for another birdie to go out in 33. He stumbled to a bogey at the 10th, but tallied a birdie at the 15th to get back to minus-6. Scott then played his second shot within a foot of the hole for a tap-in birdie at the par-4 16th.
'It was a very consistent round today,' said Scott. 'I played a lot better than I did yesterday. I'm making some nice length putts. When your confidence is up with the putter, it allows you to be a little more aggressive with the rest of your game.'
Gogel had a birdie and a bogey over his first five holes, but he ran off back-to-back birdies starting at the sixth to maintain his lead at 10 under par. Gogel struggled to a bogey at the eighth, however, and fell one shot behind Allenby with a bogey at the 12th.
He found trouble again with a bogey at the 16th to finish two shots back after a round of 72.
Westwood had a rocky front nine with two birdies, two bogeys and an eagle. He found trouble early on the back side with a bogey at the 10th, but collected a birdie at the 14th and parred his way in for a round of 69.
Elkington tallied three birdies and a bogey on the front nine to make the turn at 5 under. The former PGA champion added back-to-back birdies from the 10th en route to a round of 67.
Ernie Els posted a 67 to share sixth place with Jim Furyk, Paul Goydos, Shigeki Maruyama and Tommy Armour III at 6-under-par 136. Phil Mickelson was two shots further back in a group at 4-under-par 138.
Retief Goosen carded his second straight round of 70 to finish in a group at 2-under-par 140 that includes Vijay Singh.
The 36-hole cut fell at 1-under-par 141 with 70 players qualifying for the weekend. Among those who failed to make the grade were Stewart Cink, Peter Lonard, Justin Leonard and Tom Lehman.