The Brit-Finn pair beat the 16th seeded Indo-Swiss pair 3-6 6-3 6-2 in a well-contested three-setter.
What would be embarrassing for the Paes-Hingis pairing would be the fact that their opponents were playing the first match of the tournament having got walkover in the first two rounds.
Paes and Hingis had completed a mixed doubles Grand Slam after their French Open victory having captured the Australian Open, Wimbledon and US Open titles in 2015.
Watson and Kontinen reached the third round without getting walk-overs from Louisa Chirico and Denis Kudla in the first round followed by Bruno Soares and Elena Vesnina who also didn’t play in the second round encounter.
“We were warming up and getting ready each day and we were always put on at the end of the day, so we’ve literally just been ready to play for each match and they’ve told us last minute,” said Watson.
“I think today in the first set we were finding our ground, getting comfortable with each other, and then we kind of took off, especially in that third set.”