McDowell and Furyk took advantage of the outstanding morning conditions on day two, Furyk eventually moving into a share of second position with his round of 69 to get to 1 under par and into a share of second position with Tiger Woods before Thompson and Woods had teed off.
"Obviously I'm very happy" said Furyk after his round. "I feel great about the 69. I felt like yesterday coming down the stretch maybe I hit a couple poor putts and wasn't disappointed in the score, but I had a makeable putt on 18 and I really didn't hit a good solid putt.
"But today I feel good about the score. I kept the ball in the fairway pretty well. I hit a bunch of greens this week and could probably get a little better with my speed on my mid range putts, on my makeable putts.
"But I feel solid and in control so far, so I know obviously it's going to get even more probably firmer and faster and even more of a stern test for the weekend. So get some rest this afternoon and get prepared for and try to envision what the course may play like and get prepared."
McDowell started with a bogey but a few holes later he had moved to two under for the championship and at that point was in outright second position. He dropped shots late in his round but at 1 over he is well enough positioned.
Of the Australians who played in the morning field, John Senden was the clubhouse leader after his round of 73 has him one ahead of Jason Day whose round of 71 was impressive given his opening 75.
At 5 over Senden was in 50th position, a position which will improve considerably over the next few hours as the afternoon field battles the increasingly demanding Olympic layout.
Day is also well inside the cutline well at 6 over the cut expected to creep out to eight or nine over by day's end.
Australians who will miss the cut are two who could have been considered good chances heading into the week, Geoff Ogilvy and Aaron Baddeley.
Ogilvy added a round of 74 to be at 10 over while Baddeley's round of 79 has him at 14 over.
The leading Australian after day one, Alistair Presnell, was to tee off at 2.31 in the second to last group of the day.