The 35-year-old American climbed from joint-fourth to top of the leaderboard and on target for the $12,000,000 winner's cheque when carding a seven-under-par bogey-free 65 to move clear of both countryman Aaron Wise and world number three Cameron Smith of Australia on eight under.
Former FedEx Cup champion Horschel has never won a major but is on course to make a statement victory in Columbus having surged up the standings at Muirfield Village Golf Club.
"It's just going through our process, making sure we have a number where we're trying to land the ball, talking about the shot, the club selection, the wind," the Floridian said.
"When we do that, it allows me to have a clearer picture and have a little bit more of a higher acceptance level over the golf shot."
Horschel said he would prepare for Sunday's final day as normal in the hope of repelling the twin challenge of Wise and second-round leader Smith.
"I just go to the tee understanding I'm leading the tournament," he told reporters.
"I know I've got however many shots I have ahead of the lead. Just going out, trying to play a really good round of golf.
"I'm not going to be protective. I'm not going to be overly aggressive. I'm going to play the way I have the last three days."
Wise and Smith posted respective rounds of 69 and 72, followed one shot back by American Daniel Berger, Francesco Molinari of Italy and Venezuela's Jhonattan Vegas.
Northern Ireland's Rory McIlroy suffered bogies on 16 and 17 to leave him one over for the day and out of contention having been within three shots of the lead at the halfway stage.
Memorial Tournament third round
-13 B Horschel (US); -8 A Wise (US), C Smith (Aus); -7 D Berger (US), F Molinari (Ita), J Vegas (Ven);-6 L List, D Riley, P Cantlay, D McCarthy (all US), J Niemann (Chi).
-4 R McIlroy (NI); -3 S Lowry (Ire); -1 J Rahm (Spa), A Rai (Eng); Evens M Laird (Sco).