Seeking to add a second major title to his 2013 Masters triumph, Scott will tee off in the last group at the year's final major alongside two-time US Open victor Koepka.
A former world number one and the 2013 Masters victor, Scott muscled his way into second place on 10-under, while Spaniard Jon Rahm (66) and Americans Rickie Fowler (69) and Gary Woodland (71) were three behind. Kevin Kisner shot a six under par 64 to sit at 9 under par, one shot out of the lead.
The 38-year-old was also hot with the putter, rolling in six birdies to keep Koepka within striking distance. Woodland, even with the lowest 36-hole score in 60 years of stroke play at the PGA Championship, still had a long way to go.
Even with back-to-back bogeys on the back nine, Koepka had a 4-under 66 for a two-shot lead over Adam Scott, the 2013 Masters champion who has been struggling through his worst season in almost two decades.
Rounding out the Australian contingent is Marc Leishman (72) and Cameron Smith (73), who both tumbled down the leader board to be one over and three over respectively.
The quiet American looked set to match the largest 54-hole lead in tournament history when he bolted five shots clear after 13 holes from a large group including Tiger Woods at Bellerive.
Woods, searching for a first major win since the 2008 US Open, moved into contention after a blistering front nine which contained five birdies and one bogey.
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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 was 3 under through seven holes before a thunderstorm came in and forced golfers off the course.
With a heat index north of triple digits and the kind of humidity that makes the championship's relocation to the more comfortable confines of May starting next year a welcome reprieve, the strongest have risen to the top.
"Not just myself, but everyone's going to have to shoot low rounds", Woods said.
Koepka, who missed the Masters with a left wrist injury, opened birdie-birdie to grab the lead after playing partner Woodland made bogey at the second, but Woodland birdied the third hole to pull level.
"I've watched Tiger win 14 of these things hanging around a lot of the time", Scott said. His other birdie came at the par-5 17th, where he hit the green in two and two-putted from 30 feet. Justin Rose (-4) leads the English challenge, with Matt Wallace and Ian Poulter just a shot back.
"I feel safe because I feel safe where my game is", Woodland said.