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.
After a largely disappointing Masters and a missed cut at the US Open, this is the second major in a row in which Woods has been in contention, following his dramatic display at the Open.
England's Wallace produced one of the most memorable moments of the tournament by claiming a "mindblowing" hole in one on the par-three 16th.
That left Woods five strokes off the pace of United States compatriot Koepka, who birdied five of his first nine holes to make the turn on 13-under par, three shots ahead of Americans Rickie Fowler and Gary Woodland with Australian Adam Scott, the 2013 Masters champion, and American Kevin Kisner another stroke adrift.
The victor of the 2018 PGA Championship will take home nearly $2 million. Any player who made the cut but doesn't submit a 72-hole score will also get $3,100.
Tiger Woods birdied three of his first seven holes to get to 3 under par before play was suspended. He won in the penultimate group at the U.S. Open each of the last two years. He was six shots back of the lead heading into the third round.
US Open champion Brooks Koepka fired a blistering 63, equalling the PGA Championship record for lowest round, to leapfrog into outright third at eight under. "And that might mean shooting 5 under again to hang around, but I would love to be in the mix coming down the stretch and have the chance to hole some putts to win".
'I actually played well on the back nine in both rounds, ' insisted Woods, with good reason. "I've got to make adjustments better than I did [Saturday]". "I just wish I could have gotten myself a couple more shots closer to the lead".
"You always feel like you've got something to prove, whether it be to yourself or somebody else", said Koepka, who will take a two-stroke lead into the final round following a third-round 66.
"Obviously things haven't been going well for me this year".
Tiger Woods highlights from Rd. 2 of the 2018 PGA Championship
Those birdies after his big blunder stood out to Finau, one of only 11 players to make the cut in all four majors this year. It is only the second time in major-championship history that two scores of 63 or better have been shot in the same round.
England vs India, 1st Test, Day 2: 5 Talking Points
With just two days and a session left in the Test match, England have done well to all but take an Indian win out of the equation. While Chris Woakes and Johnny Bairstow were tormenting the Indian bowlers, Kohli had to leave his troops to treat his sore back.
Derby County team news for Leeds United visit
Lampard's first game in charge of Derby had been less impressive as they scraped a last-gasp victor at Reading . From the opening exchanges, it was clear that this game was always going to one that had goals in it.
Man Utd: Jose Mourinho finds some harmony at last - Dublin
If you have round pegs in round holes, and all of them are doing the right job at the same time, then you are going to do well. It was Shaw, who just like Pogba has endured some tough times under Mourinho , who was the unlikely late hero for United .
Tesla shares fall 5 percent amid news of expansive SEC probe
Musk and SoftBank held unsuccessful talks about a take-private deal in April 2017, according to a source familiar with the matter. Securities and Exchange Commission has since begun to make its own inquiries to check the veracity of Musk's controversial tweet.
EPL: Manchester United vs Leicester City
However, a move did not materialise and Mourinho must now work with the same central defensive setup as he did last season. Had they not got to the final of the Champions League last season I actually think they could have finished second.
Gary Neville reacts to Paul Pogba's 'weird' penalty
The France playmaker then continued to impress as the first half wore on at Old Trafford , leading his team-mates by example. With seven minutes remaining, he flicked the ball past a defender before sending a low left-footed strike into the net.