The American, seeking his first PGA title since 2019 and fourth overall, fired a bogey-free four-under par 67 to stand on 16-under 197 after 54 holes at TPC Deere Run in Silvis, Illinois.
Alex Smalley, who fired a 62, shared second on 198 with fellow Americans Adam Schenk and Denny McCarthy with American Peter Kuest fifth on 199.
Eight others were only three adrift, including 36-hole leader Cameron Young, who stumbled back with a closing double bogey to shoot 71.
"Probably (need) another round like today," Todd said. "Looks like there are a lot of pursuers there. It's a pretty bunched leaderboard so I'll have to go out there, play my game, make a bunch of birdies and see what happens."
World number 78 Todd, who has converted two of his five career 54-hole PGA leads into victories, was a runner-up at Pebble Beach earlier this year.
Todd's PGA triumphs came at the 2014 Byron Nelson Championship and the 2019 Bermuda Championship and Mayakoba Classic in Mexico.
Todd sank a 26-foot eagle putt at the par-5 second hole, then closed strong with a six-foot birdie putt at the 13th, a 17-foot birdie putt at 15 and a stunning 45-foot birdie shocker at the par-3 16th.
It took a tense 12-foot par putt at the 18th for Todd to claim the edge over his countrymen.
"Anybody who is within three shots of the lead is looking to go as low as they can, so there's certainly going to be no defence for me," Todd said. "It's going to be the same stuff."
World number 85 Smalley, who shared ninth two weeks ago at the Travelers Championship for his best finish of the year, matched his career-low PGA round to leap into contention.
Smalley made seven birdies and an eagle to give himself a chance to become the 24th first-time PGA winner in the history of the event.
"I don't see why it couldn't be," Smalley said. "Just got to go out there and if I play like I did today. I feel like I have a pretty good chance. Just got to have the same mindset."
His successes included an approach to three feet at the par-5 second to set up an eagle and birdie putts of 34 feet at the par-3 12th and eight feet at the first, fourth and 17th.
World number 19 Young, last year's British Open runner-up, birdied 16 and 17 to pull within one of Todd but found a fairway bunker and water at 18 on his way to a closing double bogey.
The 26-year-old American is chasing his first PGA Tour title after six second-place showings, including this year's WGC Match Play.
