Resuming at 169 for 2 at the Eden Gardens, Bengal willowers failed to negotiate pacers J P Yadav (4/53) and Harvinder Singh (4/75) to lose their remaining wickets by adding 109 runs in the morning.
However, a priceless 25 runs put on by the last wicket partnership of skipper Deep Dasgupta (39; 108b, 177 mins, 4x4) and S S Paul (8 not out) enabled Bengal extend their innings to 278, a lead of 19 runs over the Railways first innings total of 259.
Railways, struggling to stave off relegation to the plate division, were 140/2 at draw of stumps, with Amit Pagnis (76 batting) and S Khanolkar (24 batting) at the crease.
The visitors are now 121 runs ahead, and the morning session on the morrow will be crucial in deciding the outcome of the match.
Bengal would attempt to get the remaining Railways wickets to chase a gettable total in their bid to force an outright win.
Railways, on the other hand, seemed resigned to their fate, with skipper Sanjay Bangar saying it would be a difficult ask for their side now to remain in the elite division.