It was the Magpies' biggest home defeat in this competition since losing to Sheffield United 5-0 in January 1914.
The one-sided third round replay was all too easy for the Championship leaders who can now prepare for the visit of Reading - one of the sides who replaced them in the Premiership this season.
Two up at the break through the outstanding Gary McSheffrey and a Nobby Solano own goal, Birmingham probably feared a grandstand fightback when James Milner powered in his second of the season after 56 minutes.
But in a mad three minutes, Steven Taylor was red carded and Bruno N'Gotty made it 3-1 from the resulting free-kick.
Newcastle then all but threw in the towel as Sebastian Larsson and the hard-working Dudley Campbell added two more in the last ten minutes against an unchanged Newcastle side that had won 3-2 at Spurs on Sunday.
It took City only five minutes to go in front when an horrendous clearance from Peter Ramage went to Larsson who eventually crossed from the right. The ball flicked off the head of Ramage and dropped for £3million hit-man McSheffrey who finished with some style.
Newcastle could have argued that Campbell was offside and interfering with Shay Given - but the goal was no more than City deserved.
The home defence was all over the place in the first half. Their play was predictable and Birmingham could hardly have had an easier opening 45 minutes this season.
Matty Pattison had a couple of chances, the first a feeble effort straight at Maik Taylor and the other way over the top.
City had the better chances and Given was called upon to turn a McSheffey free-kick over the top. The former Coventry man then put a chance on a plate for Cameron Jerome who missed from just one yard out.
Campbell then beat the offside trap and he also mis-kicked before pulling the ball back for Jerome whose shot was brilliantly beaten away by Given.
Then, on the stroke of half-time, Ramage's nightmare continued when he was skinned down the right wing and the cross was turned into his own goal by Solano under pressure from Campbell.
Newcastle got back into the game after 56 minutes with a stunning 25-yarder from Milner - but then it all went horribly wrong.
In a crazy three minutes, Taylor - already booked - was shown a straight red card after pulling back Campbell. From the resulting Larsson free-kick, the ball dropped invitingly for N'Gotty and the 35-year-old defender finished with some style.
From then on it was a lost cause for Newcastle as Larsson added a fourth after 83 minutes and Campbell got the goal he deserved one minute from time.