The visitors reached the victory target of 137 without difficulty at the IAF ground on the final day.
Earlier, Sanjay Bangar-led Railways, who had a 105-run first innings lead, dismissed the hosts for 241 in their second knock. J P Yadav and Kulamani Parida claimed three wickets each.
Yadav put in a good batting performance as well, remaining not out on 52. Opener Amit Pagnis hit 41 and Bangar made 27.
Brief scores: Karnataka 194 and 241 (Sujith Somasundar 58, Dravid 38, D Ganesh 29, Robin Uthappa 25; J P Yadav 3/24, Parida 3/84, Madan Yadav 2/54) vs Railways 299 and 137 for three (J P Yadav 52 not out, Pagnis 41, Bangar 27, C Raghavendra 2/18, Ganesh 1/27).