The 14-time major champion, in the eighth month of his comeback from spinal fusion surgery after years of back injuries, shared third on eight-under-par after seven holes at Bellerive Country Club.
That left Woods two strokes off the pace of US co-leaders Brooks Koepka, a two-time US Open champion, and Gary Woodland, who matched the low 36-hole major record at 10-under 130.
Joining Woods at eight-under were second-ranked defending champion Justin Thomas, fellow Americans Kevin Kisner and Rickie Fowler and Belgium’s Thomas Pieters.
Former world number one Woods, who on Saturday morning finished off the last 11 holes of a storm-halted second-round 66, made a sizzling afternoon start, opening with back-to-back birdies and, after a bogey at five, adding two more at the par-3 sixth and par-4 seventh.
Woods, ranked 51st, won his most recent major title at the 2008 US Open and has not won any event since the 2013 WGC Bridgestone Invitational but showed solid form last month by leading Sunday on the back nine at the British Open.
Thousands of spectators watched Woods sink a 17-foot birdie putt on the first hole and drop his approach to four feet setting up a birdie at the second.
Woods answered his bogey with an 11-foot birdie putt at the par-3 sixth and a seven-footer for birdie at the seventh, the crowds and buzz around him growing with every hole.
A roar resounded across the 7,316-yard layout when Woods dropped a six-foot birdie putt at the par-5 eighth to pull level with the chase pack behind Koepka and Woodland.
Koepka opened birdie-birdie to grab the lead after Woodland made bogey at the second but Woodland birdied the third hole to pull level on 10-under.
Birdies were abundant early, a hint that scoring conditions might rival those of Friday that saw three players make a run at matching the all-time low major round of 62 by Branden Grace of South Africa from last year’s British Open.
Ninth-ranked Fowler, this year’s Masters runner-up seeking his first major title despite eight top-five major finishes, completed a morning 67 to lift himself into the hunt.
After finishing the second round, the 80 who made the cut were sent off the first and 10th tees in trios in a bid to complete the third round by sunset.
“It’s going to be a long day,” Fowler said.
Four-time major winner Rory McIlroy, whose morning 67 was highlighted by a 58-foot chip-in at 14, had three bogeys against two birdies over the first 10 holes in round three.