An organised Rovers were good value for their win, taking advantage of a passive first-half performance from the home side to secure a lead and then holding them at arm's length after the break.
Blackburn's goal came from their most productive area, down the right flank where Ryan Alebiosu and Ryoya Morishita caused Bristol City no end of problems.
Morishita had wasted a great chance in the 41st minute when he put a free header over the bar from Ryan Hedges's cross but he was pivotal in the goal.
Freed by Lewis Miller, he got to the byline and squared from Ohashi - with his head bandaged from an earlier cut - to score his third goal of the season from close range.
Although the Robins were sharper in the second period, threatening briefly through headers from Rob Dickie and Ross McCrorie, they were unable to fashion a single shot on target in the match.
Even though Blackburn lost their captain Scott Wharton and had to switch goalkeepers for the last 10 minutes when Balasz Toth limped off, they closed the game out with no alarms.
They will be at home to Derby County in a lunchtime kick-off on Saturday, with Bristol City travelling to Watford on Friday evening.