Sent into bat after Haryana skipper Virender Sehwag won the toss, Bengal had to fall back on the duo of Chandila and Shaw after the top-order failed to make substantial contributions.
Chandila made a breezy 65 off 79 balls, hitting seven boundaries, while Shaw struck 54 off 107 deliveries with the help of four boundaries and a six.
Ashish Hooda and Yuzvendra Chahal bagged two wickets apiece, while there was one for Harshal Patel at the CH Bansi Lal Cricket Stadium.
At stumps, Pragyan Ojha and Ashok Dinda were batting on 22 and 5 respectively.
Chandila shared 64 runs for the sixth wicket with Tiwary and later, Ojha joined Shaw to add 65 runs for the eighth wicket to somewhat rescue Bengal on a picth that aided the bowlers a bit.
Batting at number three, Shreevats Goswami managed 35 before getting out to Rana.