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.
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).
Among the top seven batsmen dismissed, none reached double figures and three of them – openers Sitanshu Kotak, Sagar Jogiyani and first innings top scorer Arpit Vasavada – failed to score.
Rahul Dave (5), skipper Jaydev Shah (6), Sheldon Jackson (9) and Kamlesh Makwana (7) were the other top-order batsmen to depart with single digit scores.
Agarkar took three for 15 in a fiery first spell of eight overs and Kulkarni claimed as many for same number of runs in his opening spell of nine overs. Makwana was sent back by Nayar at 34.
Kulkarni came back to grab the wicket of Sanandiya to leave Saurashtra on the brink of defeat at 53 for 8. The innings was prolonged by Unadkat and Jadeja, who put on 29 runs, before Agarkar returned for his second spell to snap the ninth wicket partnership.
Fittingly, Kulkarni came back for his third spell and ended the match by having Jadeja caught behind by Tare who grabbed his fourth victim of the innings to equal the championship season record of 41 by Uday Kaul of Punjab.
The tourists were tottering at 20 for 6 after the initial burst by Agarkar and Kulkarni and then managed to get past Saurashtra's lowest-ever score of 25 all out, also against
Mumbai at the nearby Brabourne Stadium 60 years ago.
Mumbai, who made 355 in their first innings building on the solid knock of 132 by opener Wasim Jaffer, thus regained the title after their previous successful title run in the 2009-10 season when they defeated Karnataka at Mysore in the final.
This was the seventh time that Agarkar had figured in a successful title match, this time as captain, after having been part of a triumphant squad as a player on the six occasions he had turned out in a final for Mumbai.
This morning, Saurashtra did well to grab the remaining four Mumbai first innings wickets while conceding 68 runs with Kamlesh Makwana claiming the last two wickets to fall in successive overs.