Baddeley returned from a three-hour rain delay by making three straight birdies and finished strong for a 6-under 65, giving him a share of the lead with Byrd (69) going into the weekend of the third tournament in these PGA Tour Playoffs.
But it was difficult to ignore Woods, whose second straight 67 put him one shot behind along with Barclays winner Steve Stricker (66), Justin Rose (69) and Camilo Villegas (69).
Woods is a three-time winner on this public course outside Chicago, and it was not unusual to see him make birdie on all the par 5s and wind up in the thick of contention. How he got there was not so typical.
He birdied the par-5 ninth by slicing his tee shot into the woods, pulling his second shot behind more trees and then hooking an 8-iron out of the rough to 15 feet and making the putt.
"It's all about the angles," he said leaving the green, as if that was the strategy all along.
He sliced another tee shot into the right rough on the par-5 11th, left a wedge woefully short of the hole and then made a 40-foot birdie putt, shrugging his shoulders when he slipped the putter into the bag.
And on the par-5 15th, he sent his second shot over the green into the bunker, took forever to play the shot because a butterfly kept floating in front of him, then knocked it out to 10 feet and made the putt.
"I started out hitting it great, and I felt so bad over the putts," Woods said. "Then I lost my swing and felt great over the putts. It's just one of those weird things about golf."
Baddeley and Byrd, both of whom have won on the PGA Tour this year, were at 9-under 133.
The top 30 in the playoff standings advance to the Tour Championship next week in Atlanta, and at this rate, Phil Mickelson might not have much of a lead, if any at all. Mickelson decided to take this week off after winning the Deutsche Bank Championship, but the guys lined up behind him are playing well in Chicago.
Stricker is at No. 2, and he went toe-to-toe with Woods the last two rounds and matched him birdie-for-birdie. Stricker won here in 1996 when it was the Western Open, and he might be as confident as he has ever been, especially coming off a win at The Barclays.
He walked off the green shaking his head at some of the birdies Woods was making, but his were impressive in the more conventional manner. He found the fairway and laid up nicely on the 600-yard ninth, then used the wind and spin on the soft greens to stick his wedge about 5 inches from the cup. On the 11th, he again laid up short of the green and hit wedge to 18 inches as Woods was making his from across the green.
His only big error came on the fourth, when he misjudged the wind off the tee and went into the left rough blocked by trees. There was only one limb in his way, and Stricker figured he could go under it or over it.