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 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 of the table while Derek McInnes’ City follow up consecutive wins with two straight losses.
Nottingham Forest fought back from two goals down to grab a 2-2 draw against Birmingham and preserve their own unbeaten start.
All the goals came in an entertaining second half at the City Ground.
After having the better of the first half, Forest found themselves behind courtesy of goals from Hayden Mullins and Marlon King in the space of three minutes.
Substitute Simon Cox quickly pulled one back for the hosts with a superb effort after 73 minutes before another sub, Dan Harding, levelled things up with four minutes remaining.
Charlie Austin scored two second-half goals for Burnley as they secured a 5-2 victory over Peterborough in an exciting encounter at Turf Moor.
The match was evenly poised in the first half with the score 2-2 at the interval, but Burnley fired home three unanswered goals in the second period to secure their second league win of the season and leave Peterborough still waiting for their first.
Rampant Hull made it three wins from three home games with a stunning 4-1 demolition of Millwall.
The Tigers mauled the Lions with four goals before the interval from Robert Koren, Jay Simpson, Abdoulaye Faye and Sone Aluko.
Darius Henderson grabbed a consolation for Millwall in the second half, but they were second best all afternoon as Hull leapt up to fourth.
Middlesbrough also made it three successive home wins this season by beating Ipswich 2-0.
A Luke Williams effort separated the sides until added time when Mustapha Carayol’s 12-yard effort made sure of the points.
Boro had the better of the early exchanges but Paul Jewell’s side never gave up.
Matt Mills scored his first goal for Bolton as they bounced back from two consecutive defeats to beat Watford 2-1 at the Reebok Stadium.
The former Reading and Leicester defender struck early on, and Bolton captain Kevin Davies hit a second just before the break to give the home side some breathing space.
Watford fought back in the second half and Lloyd Doyley’s cross-cum shot provided a tense finish for both sides.
Craig Bellamy curled home a superb second-half free-kick and Peter Whittingham converted a penalty as Cardiff maintained their 28-year hoodoo over Neil Warnock’s Leeds with a 2-1 victory.
Jamaica international Rodoplh Austin fired home a 30-yard thunderbolt for Leeds with 13 minutes left but it would not prove enough.
Thomas Ince gatecrashed Barnsley’s 125th anniversary celebrations with an equaliser the Tykes were pegged back by Blackpool at Oakwell.
Craig Davies had put the home team ahead with a long-range effort early in the first half, but Ince continued his strong start to the season by netting for Blackpool after half an hour.
And Danny Ward scored after just 47 seconds as a toothless Derby fell to a 1-0 defeat at the hands of newly-promoted Huddersfield.