Bopanna and his Australian partner are now 1-1 in their group and could still qualify for the semi-finals depending on the result of their match against Wesley Koolhof and Neal Skupski on Friday.
The previous oldest player to win a match at the tournament was Canada's Daniel Nestor who was 42 in 2014.
Earlier this year, Bopanna became the oldest ATP Masters 1000 champion when he won the Indian Wells doubles alongside Ebden.