Molinari began the weekend three strokes behind Darren Clarke but four birdies in the final five holes took him past the veteran Northern Irishman.
An eight-under 63, only a stroke worse than the course record, took Molinari to 15-under-par 198, a shot better than Clarke, who did his best to hold off his young adversary by posting a 67.
Francesco Molinari, the leader's younger brother, carded a 68 to lie joint third, seven strokes off the lead, with Swede Peter Hedblom, who returned a 69.
The Molinaris are trying to become the first brothers to play in the Ryder Cup, with Edoardo now on course to join Francesco on Europe's table.
Playing with Clarke on Saturday, Edoardo had caught the first- and second-round leader by the eighth hole by picking up an eagle and three birdies.
A birdie by Clarke just before the turn restored a one-shot advantage but Molinari then turned up the heat with his blistering run over the finishing stretch.
"I played great golf but so did Darren, I just holed a few more putts than he did," Molinari told reporters.
He and Francesco will now play with Clarke in the final round, and Edoardo is hoping for a spectacular shootout.
"I hope Francesco gets into contention coming down the last few holes, with Darren and me, and then it will be a great spectacle for the crowds," Edoardo said.
The Molinari brothers, who won the World Cup of golf last year, are taking it in turns to visit European Tour leaderboards this year.
Francesco, 27, lost a playoff in last week's French Open but is currently in eighth place on Europe's Ryder Cup table. A victory by Edoardo, 29, will put him on the heels of the nine automatic qualifiers.
"As far as the Ryder Cup is concerned, I have nothing to lose whether I make it or not," Edoardo said, "because I didn't expect to have any chance to be in the team." Clarke, 41, also has an extra agenda at the Scottish Open. He can earn a place in next week's British Open at St Andrews by finishing in the top five on Sunday.
A few weeks ago Clarke was wondering if his chances of winning again might be over.
"This is a far cry from how I was a month ago," he told reporters. "I'm looking forward to tomorrow and all the bonuses that might come from it."
Creamer, Yakomine share US Women’s Open lead
In Oakamont, Pennsylvania, Paula Creamer and Sakura Yokomine are tied for the lead at the US Women’s Open following the conclusion of the rain-delayed second round.
Creamer had the only sub-par round after play resumed Saturday morning — a 1-under 70 at Oakmont Country Club that left her at even par. Yokomine finished up her second straight 71. Creamer played 16 holes on Saturday and Yokomine 15.
Yokomine and Creamer are one shot ahead of LPGA Championship winner Cristie Kerr and Brittany Lang, both of whom finished their second rounds before heavy rains halted play at midafternoon Friday.
Christina Kim, who also finished up on Friday, Sophie Gustafson and Suzann Pettersen are two shots off the lead.
The third round is scheduled to begin at approximately 2:30 p.m. EDT.
Stricker set new 36-hole
record at JDC
In Silvis, Illinois, defending champion Steve Stricker broke the 36-hole record at the John Deere Classic with a two-round total of 126, which is 16 under at TPC Deere Run.
Stricker, playing in the morning, shot a 5-under 66 on Friday to take a one-stroke lead over Paul Goydos into the third round. Goydos sent a buzz through the golf world in the opening round by shooting only the fourth 59 in PGA Tour history.
Goydos couldn’t maintain the deft putting touch that had enabled him to join golf’s most exclusive club and he settled for a 3-under 68, leaving him at 127.
David Frost set the old 36-hole record of 127 in 2000.
