Fourth seeds Paes and partner Russia's [ Images ] Elena Vesnina staved off a stiff challenge from the Belarussian combination of Max Mirnyi [ Images ] and Victoria Azarenka [ Images ] to win 7-6 (3), 6-3 to advance.
They will now be up against the Australian-Russian pair of Paul Hanley [ Images ] and Alla Kudryavtseva in the last eight.
Paes has a good shot at clinching a confidence-boosting title on grass-court just ahead of the Olympics [ Images ] later this month.
Rejected by his first-choice Indian men's doubles partners for the Olympics, the experienced warhorse will seek to prove a point as his mixed doubles partner for the big event, Sania Mirza [ Images ], too had taken potshots at him before agreeing to partner him.
The players, who had criticised him so heavily, have all crashed out of their respective events at the Wimbledon, leaving Paes as the lone Indian flagbearer at the season's third Grand Slam. Paes and Vesnina were pushed hard in the match on Thursday but the duo drew from their experience to emerge triumphant.
The first set went on serve and neither of the two teams could earn a break but with a fantastic first serve, the fourth seeds had the slight upperhand which proved decisive in the tie-breaker.
The fact that Paes and Vesnina did not commit a single unforced error also tilted the scale in their favour after an opening battle of 49 minutes.
The Indo-Russian combine was clearly the better of the two pairs in the second set as they converted two break points while saving seven to seal the issue after 43 minutes.
In contrast, Bopanna and Zheng were thoroughly outplayed by their more experienced and higher-ranked rivals.
The 10th seeds were broken thrice in the opening set itself which Bryan and Raymond won in just 21 minutes.
In the second set, which lasted a little over half an hour, break points again proved decisive as Bryan and Raymond converted both the chances they earned to emerge triumphant.