The Black Cats never looked back after taking an early lead and were rarely troubled by their opponents.
The win, as easy as it was, will be a real tonic to a Sunderland side, who crashed to 3-1 Premier League defeat at away to Burnley at the weekend.
In truth, the hosts were never in any danger of coming unstuck in a similar fashion against Alex McLeish's outfit.
The Blues boss rang the changes for the cup encounter and it told as a makeshift Birmingham side looked at sixes and sevens at the back for much of the game.
That was clearly evident in the opening exchanges and was to prove very costly as they were caught out just four minutes into the clash.
Rising star and homegrown product Jordan Henderson scored his first senior goal to get the hosts off to a flying start.
Steed Malbranque found Kenwyne Jones down the right flank and the striker turned provider as he rolled the ball to Henderson, who fired home from 15 yards out.
The Blues didn't learn from their mistakes and Sunderland were 2-0 up on 22 minutes.
This time Andy Reid whipped in a cross which was headed home by Fraizer Campbell as the former Manchester United man opened his account in a red and white shirt.
For all their frailties at the back, City were also very limited in attack and the Black Cats dealt comfortably with the slightest of threats they posed in the opening 45 minutes.
The hosts, on the other hand, were far more potent going forward and Jones and Campbell both had chances to add to the Wearsiders' tally.
Still manager Steve Bruce wouldn't have been complaining at the break having seen his side dominate the first half.
The Blues were lively at the break, but it was still the Black Cats who enjoyed the lion's share of possession and attacking opportunities.
Reid, Jones and Campbell all went close in the second half, but in the end the hosts had to settle for the 2-0 win.
Just as positive as the result for Bruce was the performance of youngster Henderson and defenders Paulo Da Silva and John Mensah, who were making their first home starts for the Wearsiders.
Mensah in particular was immense both in the air and on the floor, living up to his nickname of 'The Rock'.
And the Ghana international almost capped his performance with a goal but his 59th minute effort was chalked off for an earlier foul.
Still, even that couldn't take the shine off a positive and solid display from the hosts.