Chid Onokwai grabbed his second goal in two games to put 'Side ahead on 12 minutes. The forward coolly slotting home a penalty to put Michael Walther's Sky Blues ahead.
After Oscar Mendes had levelled for Imrul Gazioutfit, Tony Cookey's ninth goal of the season 'Side 2-1 up on 34 minutes.
David Vaughan equalised for Bengal in the second-half. As the game looked to be heading for a draw, 'Side grabbed a late winner two minutes from time.
Substitute Michael Ogboin was the match-winner, grabbing his sixth goal of the season to earn a fine away win.
'Side: Will Hunt, Akil Clarke, Bradley Gayer, David Etcheri (Adegoke Adetunji), Garrett Kelly, Michael Sherwood, Bradley Joseph, Jayden Mitchell-Brown, Chid Onokwai, Darius Izukanne (Jason Fontaine), Tony Cookey
Subs Not Used: Aaron Lesta, Inesh Sunithran