The third-seeded Indian pair won 6-3 5-7 11-9 to set up a clash with second seeds Max Mirnyi and Daniel Nestor, who defeated fourth seeded Jurgen Melzer and Philipp Petzschner 6-4 6-1 in their semifinal match.
Bhupathi and Paes led 6-3 2-0 before Marach and Tipsarevic turned things around to even the match at one set all.
"We let our lead slide. It got tight, down match point, but Leander and I have been in the situation before and continued to work for each point," Bhupathi conceded.
The Austrian-Serbian combination had a match point at 9-8 in the tie-break but lost the final three points to crash out.
The final is a rematch of the semifinal clash at the Australian Open, in which Paes and Bhupathi were triumphant in three grinding sets.
Paes, who won this event last year with Lukas Dlouhy, said he is taking a relaxed approach to the finals.
"I just want to keep having fun, enjoy myself out there. We've had some good results this year, so if we keep playing like we have been all year, we should be fine," Paes said.