On a day when Australian Jason Day plunged out of contention with a quadruple-bogey at the last, Kisner eked out a one-over 72 on a Quail Hollow course that bared its teeth, despite Friday's rain and little wind.
Kisner, not the longest of hitters but unerringly accurate for the most part until he double-bogeyed the 16th and bogeyed the last, posted a seven-under 206 total, one stroke ahead of fellow American Stroud (71) and Japan's Matsuyama (73).
American Justin Thomas and South African Louis Oosthuizen were two behind heading into the final round of the year's last major.
On undulating greens, some of the hole locations were extremely difficult, with nobody on the leaderboard shooting better than the 68 by Canadian Graham DeLaet, who went six-under in a remarkable four-hole stretch to vault within five strokes of the lead.
Kisner lamented squandering the chance to eliminate more rivals. He had hardly put a foot wrong until pulling his approach into water at the par-four 16th.
"I had a chance to run away from guys and take people out of the tournament that were four or five (or) six back, and I didn't do it. Now I'm in a dogfight tomorrow and I have to be prepared for that," said the world number 25.
"I didn't make the putts I've been making the first two days and just terrible finish there.
"It feels easy until you smack one in the water and then it seems hard again."
Despite that, Kisner could capture the title in just his 12th major start.
"It's a dream to win a major. That's what I grew up practising and playing, to play on the PGA Tour and to have a chance in major championships," said the two-time tour winner.
"The way my game's progressed over my career, I like where I am, and I like having a chance tomorrow. It will be awesome to take home the Wanamaker Trophy."
Matsuyama, tied for the halfway lead, had high hopes of moving into position to become the first Japanese man to win a major.
Instead, he bogeyed the first and never got anything going, making just one birdie all day and hitting more than his share of errant shots.
But by parring the brutally-difficult final three holes, known as the 'Green Mile' with water lurking, he stayed very much in contention.
"I'm disappointed with the day I played today. However, I'm happy to be just one stroke back and still have a chance," he said.
Stroud was also still standing despite bogeying the final two holes, six days after recording his first PGA Tour victory in Reno, Nevada.
"It played very difficult today," said the 35-year-old American, who recorded his first PGA Tour victory in Reno, Nevada six days ago.
"Didn't do anything great today but I didn't do anything bad. I made some great pars and at the end of the day I've got a chance. Last week gave me an unbelievable sense of calm.
"I've never felt so relaxed on the golf course and it's a lot of the reason I'm playing so well."
Texan Jordan Spieth surrendered any chance of completing the career grand slam for at least 12 months, a double-bogey at the last leaving him 10 shots off the pace.
Pre-championship favourite Rory McIlroy was also out of contention, 11 back.
(Reporting by Andrew Both; Editing by Larry Fine/Peter Rutherford)
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