Dhawal Kulkarni's composed 87, followed by three quick scalps by former India pacer Ajit Agarkar, put Mumbai within seven wickets of defending their Ranji Trophy crown, at the Gangotri Glades cricket ground, in Mysore, on Wednesday.
Resuming at 108 for five, Mumbai piled up 234 in their second essay, thanks mainly to Kulkarni's 181-ball contribution, and set Karnataka a target of 338.
The hosts were 135 for 3 at stumps on Day 3, with Ganesh Satish unbeaten on 40 and Manish Pandey on 59.
Satish, who hit five fours in his 125-ball innings, and Pandey (71 balls, 9x4) kept Karnataka's lamp burning after they were reduced to 46 for 3 at one stage.
The hosts still need 203 runs for 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. He 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 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 the season's highest wicket taker with 47 scalps, wrapped the Mumbai innings when he had Avishkar Salvi snaffled by Amit Verma at first slip.
His 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 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 the team's hopes of winning their seventh championship title alive.
Mumbai (1st innings): 233 all out
Karnataka (1st innings): (overnight 15 for 1)
KB Pawan c Powar b Salvi 33
R Uthappa c Jaffer b Kulkarni 9
R Vinay Kumar c Nayyar b Agarkar 2
Ganesh Satish c Khanvilkar b Salvi 10
Manish Pandey [ Images ] lbw b Salvi 0
Amit Verma c Agarkar b Nayyar 8
CM Gautam c Jaffre b Kulkarni 16
Stuart Binny (run out) 13
Sunil Joshi c Sawant b Salvi 17
Abhimanyu Mithun lbw b Salvi 5
Sreenath Aravind (not out) 4
Extras: (LB-6, NB-7) 13
Total: (all out in 49.3 overs) 130
Fall of wickets: 1-10, 2-26, 3-53, 4-53, 5-58, 6-71, 7-95, 8-120, 9-120.
Bowling: Ajit Agarkar [ Images ] 12-4-30-1; Daval Kulkarni 19-2-52-2; Avishkar Salvi 13.3-6-31-5; Abhishek Nayyar 4-1-9-1; Romesh Powar 1-0-2-0.
Mumbai (2nd innings):
S Kukreja c Satish b Vinay Kumar 13
W Jaffer c Gautam b Mithun 8
A Rahane c Gautam b Mithun 4
O Khanvilkar lbw Mithun 0
A Nayar c Pandey b Joshi 50
V Samant c Satish b Mithun 10
D Kulkarni c Pawan b Vinay Kumar 87
A Agarkar c Uthappa b Mithun 4
I Abdulla c Gautam b Vinay Kumar 15
R Powar not out 28
A Salvi c Amit Verma b Mithun 0
Extras: (b 10, lb 3, w 1, nb 1) 15
Fall of wickets: 1-10, 2-18, 3-18, 4-34, 5-51, 6-146, 7-150, 8-172, 9-233.
Bowling: Vinay Kumar 25-6-78-3; Mithun 22.3-4-71-6; Aravind 15-4-40-0; Sunil Joshi 19-12-31-1, Amit Verma 2-1-1-0.
Karnataka (2nd innings):
K Pawan lbw b Agarkar 23
C Gautam c Jaffer b Agarkar 0
G Satish batting 40
R Uthappa c Samant b Agarkar 4
M Pandey batting 59
Extras: (b-4, nb-5) 9
Total: (3 wickets; 42 overs) 135
Fall of wickets: 1-1, 2-42, 3-46.
Bowling: Agarkar 12-5-26-3; Kulkarni 9-1-43-0; Salvi 10-3-36-0; Nayar 6-2-11-0, Powar 3-0-8-0; Abdullah 2-0-7-0.