Saurashtra, trailing the home team by 207 runs in the first innings, were shot out for a pathetic 82 in less than three hours and 36.3 overs, 41 minutes after tea.
Mumbai, thus, clinched their 40th national title in 44 appearances in the summit contest and their first after two blank seasons.
Agarkar snapped up four wickets for 15 runs while his younger teammate Kulkarni grabbed 5/32 to complete splendid match figures of nine for 56.
The home team pace duo finished off the lop-sided contest with their fiery first spells to help Mumbai regain the crown after a gap of two seasons by sharing six wickets equally.
The other wicket-taker for Mumbai was Abhishek Nayar (1 for 3).
Mumbai also earned the right to take on the Rest of India in the Irani Cup tie which is to be held at the same venue here from February 6-10. The home team also won Rs 2 crore as the prize money while Saurashtra got Rs 1 crore.
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The visiting team's batsmen showed a distinct lack of application and surrendered on a wicket that provided good pace, bounce and prodigious movement to the swing bowlers even on day three.
They capitulated for the second time in the match after having been bowled out for 148 in 75.3 overs in the first innings on day one to which Mumbai replied with 355.
The highest score in a dismal batting display for Saurashtra was 22 off 35 balls by Dharmendra Jadeja.
Saurya Sanandiya (16) was the only other player to reach double figures after staying for more than an hour at the crease like another lower-order batsman Jaydev Unadkat (9 in 69 minutes).