Dhawan (150no) and Vijay (89no) combined for an unbroken stand of 239 ??? beating the 175 Wasim Jaffer and Dinesh Karthik put on against the Tigers in 2007 ??? during a rain-affected day one.
Only 56 overs of play were possible due to the inclement weather but that didn???t stop Dhawan crunching his third Test ton ??? and 21 boundaries????? after India captain, Virat Kohli, won the toss and opted to bat.
Dhawan, preferred in the side to Cheteshwar Pujara, was belligerent during the 23.3 overs before the pre-lunch rain, thumping 74 runs from 71 balls against a Bangladeshi attack featuring just one frontline seamer, Mohammad Shahid.
The opener punished some loose bowling from the hosts, though he had a moment of fortune in the 24th over when Shuvagata Hom shelled a catch diving low to his left at short-midwicket.
Vijay was more circumspect than his partner ??? Dhawan had smoked nine boundaries before he had collected his first ??? but had to survive an lbw shout in the second over after being hit on his pads by Soumya Sarkar as he ended the truncated morning session on 33 from 70 deliveries.
Dhawan continued apace once play resumed at 3.30pm local time, bringing up his first Test century since notching 115 against New Zealand in February 2014 off 101 balls with a sweep for four through midwicket.
Vijay became more vibrant as the day progressed, creaming Jubair Hossain over mid-on for six, but he played second fiddle to Dhawan, who after being dropped again at short midwicket, this time by Mominul Haque, reached 150 off the last ball of the day.
India ??? skippered by Kohli following MS Dhoni???s Test retirement last December ??? had earlier picked spinner Harbhajan Singh in a Test for the first time in over two years, with Wriddhiman Saha chosen to replace Dhoni behind the stumps.