Basford bypassed Long Eaton United in the FA Youth Cup at Grange Park on Thursday evening with goals either side of half-time despite late Blues' comeback.
Lui Bull's goals either side of half-time gave Basford a two-goal advantage, and Hugo Broughton's goal direct from a corner kick turned out to be just a consolation.
Curtis Burrows made three changes to the side that overcame Holbeach United in the previous round - Phoenix Taylor was replaced in goal by Jackson Barr, with Alfie Barker and Harry Pearson earning themselves a start over Nathan Dean and Ben Dawson.
Both sides began with intent and a high intensity from the start but it was the home side that came closest in the opening two minutes.
Alans Voskresenskis drove down the right-hand side and floated a teasing cross into the six-yard box looking for the head of Matthew Gale, although Daniel Morledge was quick off his line to catch the ball and deny the forward.
Then, four minutes later, Lui Bull almost diverted a low driven strike down the other end of the pitch, if not for a diving save from Barr.
Barker had an opportunity to grab an opener for the Blues in the 15th minute - the midfielder latched onto a Broughton cross with a towering header at the back post, but the Basford shot-stopper was equal to it.
Two minutes later, Lynden Joyce came inches away with a venomous low free-kick sent towards the bottom right, although Barr did superbly to dive and push the ball around the post.
The Blues did well to maintain the constant press from Basford, but in the 44th minute, the inevitable goal came. An unmarked Bull received the ball inside the box and placed a superb strike into the bottom left, out of Barr's reach.
Basford began the second half in identical fashion to the way they ended the first, as a dangerous Bull latched onto a loose cross inside the box with a turning half volley and doubled the visitors' lead.
Bowers had a speculative effort in the 53rd minute for the Blues, although it was a comfortable stop for Daniel Morledge.
However, a goal did eventually come for Long Eaton mid-way through the second half. A corner kick taken by Broughton, with 70 minutes on the clock, looped all the way into the back of the net after Morledge misjudged his punch.
In the dying moments of the match, Ben Bowers came close with a volley on the turn inside the box, however, Basford threw bodies in the way of the strike to deny the Blues a late equaliser.
The Academy Blues continued to fight and put pressure on the Basford defence, but the visitors back line remained strong and subsequently earned themselves a place in the next round.