After the platform of an astonishing start - goals after just 13 and 90 seconds, both from Adan George - Blues never looked back.
George completed his hat-trick after the break, with Josh Andrews netting a decisive goal that restored the daylight Blues had built early on, in first-half added-time.
It's now Barnsley at home next up for Paul Robinson's side, who showed all the ingredients necessary on a heavy pitch at the Eppleton Colliery Welfare ground.
They had a nice balance, attacked with speed and gusto, were physical when required and also defended stoutly, with 15-year-old Rico Browne impressing alongside skipper Nico Gordon at centre-half.
The beginning of the game was stunning: from Sunderland's kick-off, Andrews charged down an intended ball upfield and suddenly found it under his feet, in the area.
Despite scuffing a left foot attempt, that only helped him get it onto his right foot at a better angle to fire at goal. The shot reared up off 'keeper Jack Newman and was bouncing over the line before George came in to gleefully make sure, whacking it into the roof of the net.
Those watching, like Sunderland's players, were left in disbelief a minute-and-a-half in. From a throw, Andrews chested the ball to George who moved forward on the right and hit at goal, from inside the area. Newman got a hand to it but the ball squirmed through his grasp and inched in.
Blues were rampant and after a lovely through ball by Remi Walker, George was in on goal for his hat-trick, in the 15th minute. He got bogged down somewhat as defenders scrambled back, but after the ball came back out to Kyle Hurst, he tried to punch it towards the roof of the net only for Jack Armstrong to head away from the target.
In the 32nd minute, Sunderland got a lifeline, scoring through James Foster. He took a clever backheel return pass from Joe Hugill, advanced into the area and slipped a shot inside the post, past Josh Bradley-Hurst.
Sunderland suddenly had a sniff of a comeback and moments later Lucas Powell made a vital sliding block to stop Cole Kiernan getting a shot away in a great position in the middle of Blues area.
But that was typical of Blues defensive tenacity, and when they calmed after Sunderland's most effective period, could have picked them off at will.
George stung the hands of the 'keeper with a hammered effort from distance.
In the 44th minute Blues switched play from right to left on a swift raid; Powell played the ball forward to Hurst who weaved his way into the area and cracked a shot that clipped the outside of the near post.
There was still more to come, though, in the fourth minute of first-half added-time.
Hurst, who was a real handful all evening, dribbled his way in again, to the byline, before setting Andrews up to firmly sidefoot past the 'keeper from 12 yards or so.
With the two-goal cushion restored, Blues were not as gung-ho after the interval, as Sunderland had it all to do.
They began the period with plenty of intent, Kiernan blazing a half-volley just over and Bradlye-Hurst, who was assured all game, getting behind a shot on the turn sharply.
In the 56th minute there was another big chance for Blues when a ball out of defence found George, who linked neatly with Andrews to play Josh Williams in down the right channel. Williams raced on towards goal but Newman came out quickly to parry his attempt from just inside the area.
Foster went close with a stretching touch inside the Blues area before the tie was made secure and George completed his treble, in the 72nd minute.
Substitute Amari Miller laid the ball in from the left for George to surge into the area and slot past Newman.
There might have been more goals as Hurst bent an effort that skidded just wide of the post and substitute Yoane Zohore was denied a tap-in from Williams pass by a very good defensive intervention.
And, in fairness to Sunderland, they kept giving as good as they got as Browne had to make crucial header away from goal as bodies packed the box and Bradley-Hurst came high and outfield to intercept a long ball through off the toes of an attacker.
That was the way it was for Blues, with everyone playing a part in a comprehensive win, from first kick to last.
Blues: Bradley-Hurst, Oakley, Powell, Campbell, Gordon, Browne, Walker (Chang 68), Williams, George (Zohore 81), Andrews (Miller 77), Hurst. Subs not used: Rouse, Dugmore, Finnegan, Nguepissi.