Bengal now has nine points from four fixtures, while Karnataka is languishing with three from an equal number of outings.
Resuming from their overnight 75 without loss, the visitors ended the final day on 286 for seven wickets.
The highlight of Bengal's second innings -- they made 335 in their first knock taking a 43 run lead over Karnataka's 292 -- was a fine batting display by Manoj Tewari (80) and Laxmi Ratan Shukla (78) who put on 129 runs for the sixth wicket.
Earlier, openers Subhomoy Das (43) and Arindam (36) shared an 80-run stand to give their side a good start.
For Karnataka, Vinay Kumar (3/42) and Sunil Joshi (3/67) shared the spoils.
Brief scores: Bengal 335 all out and 286 for seven (Tewari 80, Shukla 78, Subhomoy Das 43, Arindam Das 36; Kumar 3/42, Joshi 3/67) Vs Karnataka 292.