DUBLIN, Ohio, June 2, 2012 (AFP) - Levin, seeking a first tour victory, had a 54-hole total of eight-under par 208, one shot in front of overnight leader Rory Sabbatini, who posted a one-under par 71 for 209.
Rickie Fowler carded a three-under 69 to rise to third on 211, with 14-time major champion Tiger Woods alone in fourth after a one-over 73 for 212.
Woods got off to a solid start, with two birdies on the front nine at Muirfield Village.
But Woods struggled coming in, making the last of his four bogeys at the par-four 18th.
"I got a little tired at the end, but so be it," Woods said. "I had my opportunities to move up that board and I didn't do it.
"I'm still in the ballgame," added Woods, a four-time Memorial winner. "I need to grind it out and obviously post a good number (on Sunday)."
Japan's Ryo Ishikawa carded a 71 to lead a trio on 213 that also included Sweden's Henrik Stenson (71) and Jonathan Byrd (72).
Ishikawa used a local caddie and nabbed four birdies on the back nine, including three in a row from the 12th, to climb up the leaderboard.
Veteran Vijay Singh of Fiji had the other 69 and was in a group at 214.
Levin chipped in for an eagle at the par-five fifth and for a birdie, as he posted one of just three rounds in the 60s in the blustery weather.
His round put him in position to challenge again for his first tour title. He had a six-shot lead after three rounds in Phoenix earlier this year but carded a final-round 75 to finish third behind winner Kyle Stanley.
Levin said Sunday's round will show just what he took away from his Phoenix experience.
"People have been asking me that question, and I don't know yet," Levin said. "I'll be able to answer that tomorrow."
Levin got his round going early, draining a 35-foot birdie putt at the second hole.
He holed out from behind the green for eagle at the fifth, and holed out again for a birdie at the 10th, where his second shot was short.
Levin slipped back a bit with two bogeys coming in, leaving himself with a slim lead and a wealth of well-known names within striking distance.
His nearest six rivals have either major titles, US PGA Tour titles or Presidents Cup experience to their credit.
"Four shots is definitely manageable around this golf course, considering the conditions and what they're going to be tomorrow," Woods said. "A lot of guys are still in this ballgame. It'll be an exciting day tomorrow."
Leading third-round scores here on Saturday in the USPGA Tour's $6.2 million Memorial tournament (USA unless noted, par-72):
208 - Spencer Levin 67-72-69
209 - Rory Sabbatini (RSA) 69-69-71
211 - Rickie Fowler 71-71-69
212 - Tiger Woods 70-69-73
213 - Ryo Ishikawa (JPN) 72-70-71, Henrik Stenson (SWE) 74-68-71, Jonathan Byrd 71-70-72
214 - Vijay Singh (FIJ) 72-73-69, Ryan Moore 70-73-71, Andres Romero (ARG) 69-73-72, Kyle Reifers 71-70-73, Aaron Baddeley (AUS) 69-72-73, Daniel Summerhays 69-71-74, Scott Stallings 66-73-75
215 - David Hearn (CAN) 70-75-70, Matt Every 69-75-71, Dustin Johnson 71-71-73, Jim Furyk 72-68-75
216 - Justin Rose (GBR) 73-72-71, Kevin Stadler 72-73-71, David Mathis 71-71-74, Trevor Immelman (RSA) 71-70-75
217 - Davis Love 74-72-71, Blake Adams 69-77-71, Stewart Cink 71-73-73, Johnson Wagner 72-72-73, Bo Van Pelt 73-69-75, Erik Compton 67-75-75, Lucas Glover 74-68-75, Troy Matteson 72-69-76
218 - Ryuji Imada (JPN) 75-72-71, Charl Schwartzel (RSA) 73-72-73, Chris DiMarco 73-72-73, Brendon de Jonge (ZIM) 73-71-74, Steve Stricker 73-70-75