Steve Kean once again had to contend with speculation over his future this week and will have been relieved to see his side claim three points they appeared to have squandered.
Albert Adomah gave City a flying start after 48 seconds on Saturday but Rhodes linked up with Nuno Gomes to open his account before the half hour and returned the favour 10 minutes after half-time.
Stephen Pearson equalised for the hosts and Sam Baldock did likewise in response to a magnificent solo effort from fellow substitute Ruben Rochina.
But centre-back Scott Dann reacted quickest to lash home when Morten Gamst Pedersen's corner dropped on the penalty spot early in stoppage time and Rhodes made hay on the counter attack as City pushed for another leveller.
Blackburn reach the summit as just one of two unbeaten teams in the Championship, while Derek McInnes' City follow up consecutive wins with two straight losses.
Ryan Taylor returned to the Bristol City line-up to partner former Blackburn striker Jon Stead in attack, while Richard Foster deputised for the injured Mark Wilson at right-back.
Ex-City defender Bradley Orr was included in Kean's only change, Mauro Formica making way.
The home fans were sent into raptures by a goal from their side's first attack.
Stead was allowed space down the right channel to find Adomah, whose toe poke deflected into the bottom corner.
Rhodes and Nuno Gomes linked promisingly in attack as Rovers looked to responded and the former was thwarted by City goalkeeper Tom Heaton and full-back Greg Cunningham after being set up by his strike partner.
The Scotland international improved upon those near misses in the 28th minute, capitalising upon a slip from Robins centre-back Liam Fontaine to convert Bruno Ribeiro's through ball.
Either side of the goal Kean was forced into defensive changes as Markus Olsson and Gael Givet hobbled out of the action to be replaced by Martin Olsson and Grant Hanley.
Orr produced an excellent last-ditch block to deny Stead from close range as City looked to recreate their flying start to the first period, but Rovers took the lead in the 55th minute.
Dixon Etuhu combined with the impressive Danny Murphy to feed Rhodes, who turned provider on this occasion as Nuno Gomes found a composed low finish.
Just before the hour Stead headed over from Martyn Woolford's cross with his last act, as McInnes introduced Sam Baldock.
His side were level with 20 minutes remaining as Adomah danced past Olsson and Etuhu down the right to Pearson, who swept beyond Paul Robinson into the corner.
In response Kean threw on Rochina in place of Nuno Gomes and he made an instant impact with a devastating run from inside his own half, crowned with an exquisite finish into the top corner.
But fellow substitute Baldock had the final word as the Blackburn defence stood off and allowed him ample time on the edge of the area to fire past Robinson.
Both sides pushed for the win but Rovers' extra cutting edge - £8million-worth in the case of Rhodes - proved the difference.
