he 32-year-old Australian, who is chasing his first major title, fired a two-under 68 to build a decent cushion at 11 under par with strong winds forecast for Sunday afternoon.
Northern Ireland's McDowell, the 2010 US Open champion,monster beats by dr.dre tour, climbed to seven under with a 67 and was joined by America's second-round leader Snedeker, who holed a big putt across the 18th for a 73.
Tiger Woods is one shot further adrift as he tries to win a 15th major and first since the 2008 US Open.
The 36-year-old, who won the last of his three Open titles in 2006, had to fight hard for his level-par 70 after dropping two shots in his first three holes. Woods has never won a major tournament when trailing going into the final day.
South Africa's Ernie Els (68), the 2002 Open champion, and America's Zach Johnson (66), who won the Masters in 2007, finished on five under.
Denmark's 22-year-old Thorbjorn Olesen took 71 in the company of Woods to end four under on his own.
World number one Luke Donald carded a 71 to end one under, the same deficit that Paul Lawrie overturned to win the Open at Carnoustie in 1999.
Third-ranked Lee Westwood also took 71 to slip to four over, while Northern Ireland's world number two Rory McIlroy compiled a 73 to end five over.
"I'm feeling great, it was a good solid day and I did what I needed to do. I've never played in the final pairing at a major,monster beats by dr.dre solo hd," said Scott, who is bidding to be the first Australian to win the Claret Jug since Greg Norman at Royal St George's in 1993.
"A four-shot lead doesn't seem to be very much this year on any golf tournament that I've watched.
"But I'm in a great position and hopefully a good round of golf will make it hard for the other guys.
"It's almost impossibe not to think about playing tomorrow but I'll do everything I normally do."
Scott described caddie Steve Williams,Beats By dre, who took over his bag after being sacked by Woods in July 2011, as "a great motivator" and said he could prove invaluable on Sunday.
"I'm sure there's going to be a time when I'm going to lean on his experience and he's going to have some great advice for me on how to tackle a certain situation," said the world number 13, whose best finish at a major was tied second behind Charl Schwartzel at the 2011 Masters.
Scott, who led after round one, began the day one shot behind playing partner Snedeker and inherited the lead at nine under when the American dropped shots at the fifth and sixth. After 11 holes Scott had reached 12 under and held a five-shot lead over Woods, who had fought back with birdies at six, seven and nine.
Despite dropping a shot at the 13th, the Australian parred his way home as Woods, who made several crucial par putts, dropped a shot at the 15th. Snedeker birdied 16 and 18 to claw his way back into contention and McDowell picked up three shots in his last six holes.
Despite Lawrie's heroics in 1999, when he won from 10 back, Donald said hoping for a repeat was unrealistic.
"There's a strong wind forecast for tomorrow [Sunday], but any more than six back is going to be tough to make up," said the Englishman, who is still searching for his maiden victory in a major.
"It would need quite a few people going backwards."
McIlroy, who has been struggling with his form of late, blamed his performances on an "inconsistent swing".
He said: "It [the swing] was good and then all of a sudden I just started not to really trust it. It just sort of spiralled from there.
"To be honest I'm getting used to it. The last few weeks haven't been so great."