Unseeded Bhambri and Sela pipped the Austrian pair 7-6(6) 6-7(7) 10-3 in the opening round of the euro 127,000 grass court tournament.
It turned out to be a nerve-wracking contest in which Bhambri and Sela finally prevailed when they converted their third match point after one hour and 45 minute contest.
Bhambri and Sela saved all three breakpoints they faced before taking the first set via tie-breaker.
They had a match point in the 10th game of the second set but the top seeds saved the deciding point to make it 5-5. Bhmabri and Sela then saved a set point at 5-6 and had second match point at 6-7 but the resolute Austrians again held nerves to deny Yuki and Sela a straight set win.
Yuki had yesterday won his opening singles round against local wild card Jay Clarke 7-6(2) 6-1. He faces fourth seed Italian Thomas Fabbiano in the pre-quarterfinals.