Eight of the Citizens side who started against Arsenal on Saturday sat this one out and Sven-Goran Eriksson gave debuts to Shaleum Logan and Gelson Fernandes.
Squad management on this scale was not without its risks, but the quality was there to smooth away the odd blemish or two.
The bold running of his front pair the Belgian Emile Mpenza and the Italian Bianchi was helped at times by a rather mundane Bristol City midfield.
They are still adjusting to the pace of the Championship and the demands of Premiership opposition threatened to be too much.
It said much for the concentration of their most experienced defender, Louis Carey, that only one goal separated the sides at half-time.
This came in the 16th minute when Bianchi outwitted his marker to set up Mpenza who blasted a left-footer high into the net.
The finishing of the Manchester pair was at times careless, notably early in the second half when Bianchi flashed a shot wide of a very inviting net.
Bristol had been offering little: A Scott Murray early chip into the arms of Joe Hart and a tricky shot by Lee Trundle from just outside the area which the England Under-21s keeper did well to turn over.
The Championship side perked up in the second half when they sent on Irish international Ivan Sproule and Hart made a brilliant save to keep out a left-footed effort from Michael McIndoe.
But on 68 minutes McIndoe's free-kick was swept past Hart by full-back Bradley Orr and saw the home side level.
For 12 minutes it was game-on with Bristol doing most of the pressing, but then a clinical drive by Bianchi put the Premier League side on the way into the third round draw.
