Ahead of Saturday's return to league matters, Blues came together to dump the Dons out at the third-round stage courtesy of a devastating four-minute spell at St Andrew's on Tuesday night.
Deadline-day signing Alexander Hleb, making his home debut, netted the game's opener midway through the first half before Nikola Zigic - also with his first goal for the club - and Craig Gardner quickly made it 3-0 to all but end the contest.
Substitute Aaron Wilbraham netted a deserved late consolation for a spirited Dons side to make it 3-1 at the final whistle, but Blues' progression into the fourth round was never really in doubt after the half hour mark.
McLeish made a total of nine changes for the encounter as he called on his squad to prove their worth and show what they can offer ahead of Saturday's Premier League home clash against Wigan.
And he was not disappointed as Zigic, Jean Beausejour, Martin Jiranek - and Hleb, who kept his place from the XI at West Brom - all impressed.
"It was a wee surprise in terms of our goalscoring exploits," admitted McLeish.
"We were clinical in that spell and there was a fair bit of quality on show as well with Beausejour, Hleb's finish and Zigic finally getting on the scoresheet.
"That will do Zigic good tonight, although maybe he could have had a hat-trick.
"We were delighted with Beausejour's contribution, his use of the ball for the second goal. That third goal was great as well from Gardner.
"It gives me food for thought, we've seen some pretty good performances tonight.
"But it was more important we got these guys some minutes towards their full sharpness."
It is the first time McLeish has guided the midlands club into the fourth round of the League Cup since taking charge at St Andrew's.
The Scot sees no reason why Blues should not be taken as serious contenders and will be hoping Saturday's draw is kind.
"Why not?" he said. "We've had the luck of the draw so far with two teams from a lower division (Rochdale and MK Dons) but both of those teams were a credit to the Football League.
"I see more and more young coaches encouraging the ball-playing side of the game."
Dons were certainly no pushovers, despite the convincing scoreline.
The League One side passed the ball around with confidence and had more than their fair share of chances themselves to make a good game of it, with clinical finishing proving a key difference between the two sides.
And despite being up against it, their spirited second-half display was finally rewarded with Wilbraham's late effort - much to the joy of nearly 1,200 travelling supporters.
Manager Karl Robinson said: "They gave themselves and the football club credit - the passion we showed tonight, the enjoyment and love for the game shone.
"It was a good game to play in against a very, very good Birmingham team.
"I've got nothing but praise (for my lads).
"If you keep doing what you're doing and keep playing football then you won't go far wrong.
"I'm just happy when we conceded three goals - a lot of teams would have crumbled - and I don't think that was the case with us.
"We kept moving the ball and kept doing the right things.
"I want to stress that if our players keep doing that at our level then we can cause an awful lot of damage. It's important to keep believing that we're doing the right things."