Bowyer and head of youth Terry McPhillips were this week informed they would remain in charge of first-team affairs until the end of January following impressive wins over Barnsley and Nottingham Forest in the wake of Henning Berg's sacking.
Derek McInnes' struggling Robins presented few obstacles to them making it three out of three, with a sparse Ewood Park crowd of 5,504 in attendance to see Danny Murphy fire his second Rovers goal in the seventh minute.
City offered little by way of an attacking threat and Blackburn had deserved breathing space with 58 minutes played as Grant Hanley capitalised on some haphazard defending.
Diogo Rosado started as Josh King dropped to the bench in the only alteration to the Rovers line-up, while defenders James Wilson and Louis Carey returned to a Bristol City side that lined up in a 3-5-2 formation and featured midfielder Stephen Pearson and forward Ryan Taylor.
Blackburn were sharply out of the blocks and, after Rosado narrowly failed to connect with a dangerous cross from right-back Adam Henley, Murphy fired them ahead.
The former England international collected a loose pass from Mark Wilson, advanced towards the City area and lashed a rising shot from 25 yards that caught out goalkeeper Tom Heaton.
The visitors looked for a swift response and former Rovers striker Jon Stead might have done better when Taylor headed Mark Wilson's cross back across goal.
Heaton was far more alert in the 13th minute, extending himself fully to tip Colin Kazim-Richards' clever effort with the outside of his foot around the post.
Carey put in a vital challenge as Rovers' top scorer Jordan Rhodes threatened to break clear and Kazim-Richards collected Ruben Rochina's crossfield ball to clip the top of the netting as Bowyer's men remained on top.
Blackburn's momentum as interrupted after the half-hour when Henley hobbled out of the action and was replaced by Simon Vukcevic, with Jason Lowe reverting from central midfield to full-back.
In first-half stoppage time, home goalkeeper Jake Kean was forced into a good save as Taylor nodded goalwards from Liam Fontaine's header on.
Rochina had a shot deflected wide from a Murphy free-kick early in the second half, which was largely low-key until Rovers extended their lead before the hour.
Murphy's corner was cleared as far as Rochina, who chipped towards Scott Dann and the ball fell for centre-back partner Hanley to bundle home.
The introduction of Morten Gamst Pedersen meant Vukcevic was now operating at right-back, where he made the most of unfamiliar surrounds to launch a barnstorming run in the 75th minute, drawing an assured stop from Heaton at its conclusion.
Martin Olsson, the more conventional Blackburn full-back on display, twice came close to adding a third before Martyn Woolford sliced wide on a rare foray forward from City.