The Mumbai captain remained unconquered on 107, laced with 14 fours, after helping the home team recover from a difficult pre-lunch period through an invaluable 117-run partnership for the seventh wicket with hard-hitting spin partner Ramesh Powar, who made 65 with eleven fours.
The overall lead for holders Mumbai, who led Karnataka by 126 runs on the first innings, was 390 at stumps on day three.
Bahutule was given a reprieve by umpire H S Sekhon after being declared out caught at slip off Sunil Joshi when trying to sweep the Karnataka left arm spinner. The Mumbai captain, then on 96, stood his ground and indicated to the umpire that the ball had gone off his arm.
Sekhon, to the surprise of everyone concerned, conferred with square leg umpire S C Gupta and reversed his decision which was hotly contested by the Karnataka fielders, but to no avail.
Bahutule then hit his 13th four to complete his hundred in style in 209 balls before remaining unconquered. He also added 65 runs for the eighth wicket with Vinayak Samant (29).
Joshi, who took six wickets in the Mumbai first essay, was once again the chief tormentor with three wickets to his credit.
Scores: Mumbai 292 and 264 for 8 (R Powar 65, S Bahutule batting 107; S Joshi 3 for 103). Karnataka 166.