After posting 348 in their first innings, Railways exploited the seamer friendly conditions well to restrict Bengal to 153 for four at stumps at the Karnail Singh stadium.
J P Yadav, who top scored for Railways with 93, served his side well with his medium pace to return two crucial wickets while rookie pacer Santosh Saxena accounted for the other two.
Bengal, who slumped to 113 for four before an unbeaten 40-run partnership between skipper Rohan Gavaskar (24) and Laxmi Ratan Shukla (22) steadied the innings, were still 195 runs behind with six wickets intact.
"At the moment we are not looking for an outright win. A first innings lead is what we are aiming for right now. If we manage that it will be a good thing," Bengal coach Karsan Ghavri said.
But taking the two points on the basis of first innings lead seems a herculean task for the visitors whose batsmen struggled to come to terms with uneven bounce of the track.
"In the morning the pitch was a bit damp, but the pitch improved as the day progressed. Towards the end, however, the ball was keeping low," Ghavri said.
"We are pinning our hopes on Gavaskar and Shukla besides the late order batsmen, most of whom can bat."