Delbonis, who is ranked 237th in the world, made the breakthrough in the opening set when he snatched a break of serve from Tipsarevic. However, the Serbian broke back instantly to force the tie-break.
After an early mini-break for Tipsarevic, Delbonis held his own to draw himself level before the world number eight found a decisive second mini-break to take the tie-break 7-5.
There was again very little to separate the two players in the second as neither dropped a service game.
Delbonis took control early in the tie-break and was able to hold his nerve to fend off a Tipsarevic comeback and win it 8-6.
Despite a strong showing from Delbonis, Tipsarevic showed his quality in the deciding set as a break of serve saw him take the set 6-3 and claim the match.