Herron ended at 10-under-par 200 and was joined in the lead by second-round leader Rod Pampling, who managed an even-par 70 in round three.
Australians Nathan Green (67) and Peter Lonard (69) share third place at minus-9 with Sweden's Richard S. Johnson (68).
Americans Bo Van Pelt (67) and Charley Hoffman (71) are tied for sixth place at 8-under-par 202 with Norway's Henrik Bjornstad, who carded a 1-under 69 Saturday.
Herron got going at Colonial Country Club with a birdie on the par-5 first. He climbed within one of the lead as he birdied the sixth.
The three-time PGA TOUR winner came right back with a birdie on seven to join Stewart Cink in the lead at 11 under.
Herron found the right trees off the tee at the 10th and that led to a bogey, but he still had a share of the lead as Cink had bogeyed the eighth. Herron recovered his lost stroke with a birdie on 14.
It was not a typical birdie, either. Herron found a greenside bunker with his approach, then flew his bunker shot into the cup.
Herron bogeyed 16 and 17 to fall out of the lead, as he was unable to save par on either hole after missing both greens. Herron hit only nine of 18 greens on the day.
'It worked out on 14. I visualized holing it, but not flying it in the hole,' Herron said. 'I pushed my shot on 16 a little bit. I had a chance to make par though and that's what I did today.'
At the last, Herron stuffed his approach to 2 feet and kicked it in for a birdie and a share of the lead.
'I kept it in play,' Herron said. 'I got it going a little bit early and then just kind of hung on for dear life. I birdied the last hole and that made me feel a little bit better.'
Pampling slipped to 9 under with a bogey at the first. He moved back to even-par for the day with a birdie on the third.
The Australian dropped two off the pace with bogeys on seven and 10. Pampling started to climb back into it with a birdie on the 11th. The two-time TOUR winner got back to 10 under with a birdie on the 15th before parring the final three holes.
'I got off to a really slow start with that first hole,' acknowledged Pampling. 'I just hung in there all day and didn't give up. It's a golf course that you don't need to shoot low numbers on the weekend. You don't want to shoot yourself in the foot on Saturday. We hung in well.'
Nick O'Hern posted a 2-under 68 to move to 7-under-par 203. He was joined in ninth place by Fredrik Jacobson (70), Dean Wilson (71) and first-round leader Cink (72).
Former PGA champion David Toms is among nine golfers one stroke further back at minus-6. He stands alongside Steve Flesch, Robert Allenby, Woody Austin, Chad Campbell, Zach Johnson, Jerry Kelly, Arron Oberholser and Vaughn Taylor.
Defending champion Kenny Perry is tied for 24th at 4-under-par 206 after his second straight round of even-par 70.