Pandey (69 not out) and Nair (78 not out) stitched 142 runs for the unbroken fourth-wicket stand as Karnataka overhauled the target of 184 with 22.3 overs to spare at the NSC Ground here.
Pandey's unbeaten 69 came from 58 deliveries and included 10 hits to the boundary while Nair struck 11 fours and a six in his 65-ball knock of 78 not out.
Chasing a small target, Karnataka were though in trouble as they were reduced to 43 for three in the eighth over before Pandey and Nair steered their side to 185 for three in 27.3 overs.
For Goa, Sagar Naik grabbed two wickets for 58 runs while Buddhadev Mangaldas took one wicket for 26 runs.
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Earlier, Goa produced a disappointing batting show as they were all out for 183 in 40.2 after electing to bat.
Darshan Misal was the only significant contributor with a 50-ball 51 while Keenan and Robin D Souza made 27 each.
For Karnataka, Vinay Kumar, Udit Patel and Karun Nair grabbed two wickets apiece while Abhimanyu Mithun, H S Sharath and Shreyas Gopal took a wicket each.
Brief Scores:
Karnataka: 185 for 3 in 27.3 overs (Manish Pandey 69 not out, Karun Nair 78 not out; Sagar Naik 2/58).