Resuming at 108 for five, Mumbai piled up 234 in their second essay, thanks mainly to Kulkarni's 181-ball contribution, to set a target of 338 before the hosts.
Karnataka were 135 for three, with Ganesh Satish unbeaten on 40 and giving him company was Manish Pandey (59 not out ), when stumps were drawn on penultimate day's play. Satish, who hit five fours in his 125-ball innings, and Pandey (71 balls, 9x4) kept Karnataks' lamp burning, who were at one stage in a spot of bother after being reduced to 46 for three. The hosts' still need 203 runs to score a come-from-behind victory.
Earlier, promoted up the order to stop Abhimanyu Mithun from running through the Mumbai batting, Kulkarni showed that he has makings of a sound batsman as he played with poise and purpose on a sporting deck. Kulkarni was associated in a 95-run partnership for the sixth wicket with Abhishek Nayyar (50), who fell to an outstanding catch by Pandey at long-on area off veteran left-arm spinner Sunil Joshi.
Kulkarni was also involved in a 61-run stand with Romesh Pawar (28 not out) before playing R Vinay Kumar into the hands of KB Pawan at gully.
Mithun, who finished with figures of six for 71 to emerge as season's highest wicket taker with 47 scalps, wrapped up the Mumbai innings when he had Avishkar Salvi snaffled by Amit Verma at first slip. Mithun's statemate Vinay Kumar, who bagged three wickets, swelled his season's tally to 46.
Karnataka then made a disastrous start, losing M Gautam (0) to a horrendous slash at a distant Agarkar delivery. But Pawan (23), who struck four delectable boundaries during his 23, and Ganesh Satish raised hopes of a Karnataka fightback.
They had raised 41 runs for the second wicket before Agarkar, returning for a second spell, trapped Pawan right in front of the wicket. Hardly had the 8000-strong crowd recovered from Pawan's sudden exit, the sinewy Mumbaikar sent Robin Uthhapa (4) back to the hut in his next over.
At 46 for three, Karnataka were in the doldrums. But Satish and Pandey applied themselves to the task to keep Karnataka in the reckoning of winning their seventh championship title.