Agbonlahor came off the bench in the second-half to score his first goal since February 2016 and his fifth overall against the Villans' bitter rivals to inspire them to victory in a scrappy encounter.
The game had lacked chances before his introduction. Che Adams should have done better with Lukas Jutkiewicz's by-line cut-back before the break but that was the first-half's only real opportunity.
Villa's toothlessness and Birmingham's resilience at the back created an uneventful affair, but the Second City derby finally came alive thanks to match-winner Agbonlahor - who leaves the Blues lurking just two points above the Championship relegation zone.
Villa's victory, which means they are on their joint-longest unbeaten league run against their Midlands rivals since their first 10 meetings, moves them into 12th.
Redknapp makes three changes in first game as Villa change five
Without 19-goal striker Kodjia due to his one-match suspension, £12 million January addition Scott Hogan led the line alone for Villa as part of five changes.
Local lad Jack Grealish kept his place in the starting line-up after scoring his first goal since December in the defeat to Fulham on Easter Monday.
Former Blues boss Steve Bruce switched from a 3-5-2 to a 4-4-1-1 with Leandro Bacuna, Albert Adomah, Henri Lansbury, Neil Taylor and Alan Hutton all coming in.
Redknapp made three changes from the team that lost to Burton Albion on Monday, Jonathan Grounds, Jacques Maghoma and Maikel Kieftenbeld all coming in.
The 70-year-old switched from the 3-5-2 they used in Gianfranco Zola's final game to a more traditional 4-4-2 with Krystian Bielik, Robert Tesche and Cheick Keita all dropping to the bench.
Both sets of supporters respectfully paid tribute to former Villa defender Ugo Ehiogu before kick-off, the 44-year-old coach having sadly passed away earlier this week after collapsing at Tottenham Hotspur's training ground.
But the white-hot atmosphere quickly returned inside an electric Villa Park and the two teams wrestled for control early on.
Redknapp had spoken about getting his team "back to basics" beforehand and so it proved in a dull first-half desperately lacking in any action of note.
Chances were sparse across a cagey opening 30 minutes, though Birmingham's defensive organisation was impressive given the lack of time Redknapp had with his time - appointed Zola's successor only five days ago.
Che Adams wastes uneventful first-half's only scoring opportunity
The home side enjoyed more of the possession but struggled in the final third and failed to forge chances, Hogan flicking a header wide from Bacuna's cross in their only real attempt on goal.
The visitors had a number of set-pieces but failed to trouble from them as Craig Gardner's team-mates failed to get on the end of his corner-kick or free-kick deliveries.
Villa fans became increasingly irate at referee Simon Hooper's decision-making as the Wiltshire official let go a number of shirt-pulling incidents. They were almost frustrated further by one particular instance on 38 minutes.
Ryan Shotton appeared to have hold of Hogan inside the box but Hooper played on and Birmingham countered. Alan Hutton's excellent sliding challenge on Maghoma allowed the ball to fall for Lukas Jutkiewicz.
The striker raced to the by-line and lifted a ball back into the box where Che Adams could only side-foot volley over the bar with the best chance of the first 45 minutes.
Almost immediately up the other, Bacuna drilled a dangerous cross through a crowd of Birmingham bodies in the box though with no Villa player to get on the end of it at the back post as the supporters cried out for the midfielder to shoot.
Agbonlahor changes the game off the bench
The absence of Kodjia left Villa's front-line blunted, the Ivorian having scored in 10 of their 15 wins this season and winning 24 points alone with his goals.
Bruce's side went eight without a win in January when Kodjia was on international duty with the Ivory Coast and despite Hogan's pedigree, it appeared they had yet to find an answer in his absence. But off the bench came the threat they needed.
Bruce looked to Agbonlahor, with four goals in nine Second City derby appearances before this, to inject some threat into Villa's attack just before the hour, replacing Grealish to a rapturous welcome.
Agbonlahor thundered into a challenge inside a minute, sparking contrasting reactions from both sets of supporters, and his bite and commitment sparked the game into life, though it also earned him a yellow card after a spat with Shotton.
Captain James Chester headed over from a free-kick soon after and at the opposite end, David Davis' shot on the turn forced a low fingertip save from Sam Johnstone - Birmingham's first shot on target of the afternoon.
The away team had shown impressive organisation at the back in comparison to recent displays, but the defence that had kept just one clean sheet in their previous 14 Championship fixtures was undone again by none other than substitute Agbonlahor.
The ball bounced around inside the box after a corner before falling for the 30-year-old to lash past Tomasz Kuszczak for his first goal in 14 months, sending Villa Park into delirium. That also made him the club's third-highest goalscorer in the history of this fixture with his fifth goal in 10 games against Birmingham.
Blues unable to muster response, extending wait for league derby win
Redknapp's Birmingham looked to respond but Villa held their own excellently at the back, a sublime leaping header from Nathan Baker emphatically clearing danger on one occasion.
The Blues having only scored 42 goals in 43 league games before this struggled to muster a testing response - Johnstone punching clear a Davis header - and they had to settle for a result which leaves them without a win in 10 league games - and 12 years - against Villa.
Defeat leaves Birmingham in 21st, two points above Wigan Athletic in the drop zone with two games to play. Villa climb one place to 12th, level with 11th-placed Preston North End but with an inferior goal difference.
Redknapp has only once won his first league game in charge of a new club from seven previous jobs in management, including both spells with former club Portsmouth.
The experienced Englishman will hope he can bring a reaction from his players after another disappointing result as they threaten to slip into the third tier.