Jonathan Kodjia’s eighth goal of the season was enough to seal maximum points at the expense of Wolves.
The Frenchman rose to head home Elliott Bennett’s cross in the final minute of the first half in a game in which the hosts were rarely troubled.
A match of few chances saw City create the better of them, but it was the discipline of their defending and maintaining of possession that was perhaps more impressive.
Steve Cotterill sprung a surprise with his team news, breaking up a strike force that had started every match in league and cup so far this season.
It meant a rest for Aaron Wilbraham as Kieran Agard took the captain’s place alongside Kodjia, while Nathan Baker recovered from the hamstring strain that saw him miss Saturday’s defeat to Fulham, earning a recall at the expense of Joe Bryan.
City started well, with Marlon Pack trying his luck from 25 yards with an early sighter before Agard helped the ball around the corner for Williams to race into the box.
But as goalkeeper Emiliano Martinez advanced, the Irishman seemed caught in two minds and found neither the bottom corner nor the waiting Kodjia, as Wolves escaped.
Cotterill had highlighted the counter-attacking danger of the visitors before the game, but it was from a set-piece that Wolves first threatened.
Defender Mike Williamson, on loan from Newcastle United, stayed forward after City had cleared the initial corner and tried his luck from 20 yards with a fierce shot bravely blocked by Baker.
As an overall spectacle it was a far cry from the helter-skelter start against the Cottagers, but stand-in skipper Korey Smith made his mark with some typical mopping up on the edge of his own box before City countered at pace.
Williams released Luke Freeman to cross the halfway line with purpose before the ball eventually found its way back to Smith, who warmed the gloves of Arsenal loanee Martinez midway through the first half.
Freeman would become increasingly involved, firing over from Bennett’s short free kick before latching on to Marlon Pack’s pass inside the full-back only to send his low cross into the arms of the stooping Martinez.
It had not been a classic but City had stayed patient and done a fine job of restricting their visitors, opening the scoring with a goal perfect both in its timing and execution.
Pack’s raking cross-field pass was collected by Freeman, who found Agard with his back to goal. The striker duly laid the ball off for Bennett to cross from the right towards the back-pedalling Kodjia, who showed remarkable power to head home from six yards.
Wolves boss Kenny Jackett was clearly unimpressed with what he had seen and responded with a double change at the interval to match up with City’s 3-5-2 formation.
On came experienced duo Grant Holt and Adam Le Fondre – with over 300 league goals between them.
It would not take long for their attacking instincts to come to the fore. Le Fondre embarked on a long run down the right flank and squared the ball for Holt, whose shot was parried only to Dave Edwards to prod home before the offside flag intervened.
Agard led the City response with a snapshot that unsettled Martinez, suggesting a more frantic second period lay in wait.
But the hosts continued to run a tight ship and kept the ball extremely well. Martinez was forced into low saves to keep out Kodjia, Freeman and Pack whereas Frank Fielding remained a virtual spectator.
Cotterill’s men would have to be resilient in the face of late pressure, but visiting goal attempts were still conspicuous by their absence and a late penalty appeal was waved away as City held firm to secure a third clean sheet in five games.