Agarwal smashed 13 boundaries and three sixes in his explosive knock to help Karnataka post a huge 312 for nine at Chinnaswamy stadium.
Mayank shared a useful 94 runs partnership for second wicket with inform Lokesh Rahul (40) as the duo consolidated the innings after the fall of Robin Uthappa's (27) wicket.
Following Rahul's dismissal, Manish Pandey also played a crucial role as he added 70 runs for third wicket with Mayank.
A R Yadav was the most successful bowler for the visitors with figures of three for 54 and Shadab Jakati two for 52. H H Gadekar, S A Badiuzzmama and A Garg bagged one wicket each.
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In reply, Goa were bowled out for 241 even as Sagun Kamat (63) and D W Misal (42) put up a brave front. They knit together a 58-run stand for the sixth wicket.
No other Goan batsmen could resist the Karnataka bowlers well as the visitors failed to build partnerships, which was crucial in chasing a 300-plus target.
In the second match, Andhra Pradesh sprung a surprise as they overwhelmed traditional arch-rivals Hyderabad by six wickets.
Electing to bat, Hyderabad could manage a paltry 166 in 47.5 overs with Habeeb Ahmed and Hanuma Vihari scoring 44 and 43 each.
S B Dasari ran through the Hyderabad innings with a match-winning figures of four for 21 in 4.5 overs. Dasari was well supported by P Vijay Kumar who claimed two wickets after conceding 37 runs.
In reply, Andhra chased the target at the expense of just four wickets and with 59 balls to spare.
Tamil Nadu and Kerala game was abandoned due to rains.