Scot Fleming and Yorkshireman Marray defeated sixth seeds Rohan Bopanna and Edouard Roger-Vasselin 6-4 6-4 in the third round to reach their first grand slam quarter-final together.
Fleming reached quarter-finals at Wimbledon and the US Open in 2011 with his regular partner Ross Hutchins, who has been off the tour this year receiving treatment for cancer. Hutchins is now in remission.
Marray, of course, won the Wimbledon title last year with Dane Freddie Nielsen but had never been past the third round at any other slam until now.
World number one team Bob and Mike Bryan are going for a grand slam of all four major titles in one year but they were close to going out in the third round.
The 35-year-old American twins trailed by a set and a break against Canadians Daniel Nestor and Vasek Pospisil but fought back to win in three sets.
Fleming and Marray will make their debut on the Arthur Ashe stadium court on Monday, with the match scheduled last on in the night session.