The lads maintained their fine league form - six wins on the trot in the Barclays U18 Premier League - with a convincing performance and victory in this third round tie.
Belgian youth international Azzaoui, 16, lit up Victoria Road with a treble that would have graced any occasion.
The first was a cool, curling finish with only two minutes on the clock, the second a solo run and finish just 20 seconds into the second half and the third a 25-yard dipper to put the icing on the cake of the 4-1 win.
The first half was lively - as these ties always are - and exploded into life inside two minutes.
Shayon Harrison won possession on the edge of the Rovers box and rolled in to Azzaoui who curled exquisitely into the far corner from 16 yards.
Rovers responded immediately. Tom Glover got down well to keep out Connor Mahoney from the right angle on four minutes but it was 1-1 minutes later. Ryan Nyambe dropped a free-kick into our box from halfway, we failed to clear, Sam Lavelle hammered against the crossbar and Sam Joel was there to bury the rebound.
As the game settled, we started to make inroads down the flanks. Kyle Walker-Peters hit the byline only to see his cross evade everyone and Onomah did exactly the same from the left with the same result on 15 minutes.
The next chance arrived on 23 minutes when Anthony Georgiou's shot deflected into the path of Harrison, who fired at goal but saw his effort blocked by Nyambe.
The impressive Onomah restored the lead on 29 minutes. Georgiou was involved again as Onomah walked onto his cross from the right and volleyed straight at Andrew Fisher, who did well to palm out but back into Onomah's path and the finish this time was clinical.
Joel glanced a half-chance wide on 39 minutes and the final action of note saw Onomah create something out of nothing two minutes from the break, nicking the ball from Nyambe on the left touchline, jinking past two defenders on his way into the box only to fire straight at Fisher.
Azzaoui stamped his mark on the game again with a goal to remember just 20 seconds into the second half. Picking the ball up on halfway, he took off on a run and his sheer pace took him past four players before skipping around Fisher and slotting home from the tightest of angles.
Harrison was inches away from the fourth goal on 54 minutes. Onomah started the move, Azzaoui played a reverse pass to the striker whose shot cannoned back off the post. Walker-Peters then took off down the right, drove to the byline but aimed his cross too near Fisher.
We continued to press as Georgiou found Cy Goddard who cushioned a pass into Onomah, his shot blocked this time. From the corner, Onomah latched onto the loose ball again and this time fired just wide, 68 minutes on the clock.
Rovers substitute Lewis Mansell almost scored with his first touch a minute later, heading over from Jack Doyle's inswinging corner.
Azzaoui completed a night to remember with a goal worthy of his hat-trick on 85 minutes, this time picking the ball up centrally and driving towards goal before letting rip from 25 yards, his effort dipping viciously under the crossbar.
Spurs: Glover, Walker-Peters, Muscatt, Amos, Carter-Vickers, Walkes, Georgiou (Loft, 81), Onomah (C) (Stylianides, 76), Harrison, Goddard (Ross, 88), Azzaoui. Unused subs: Voss (GK), Sterling.
Blackburn Rovers: Fisher, Nyambe, Doyle (C), Pierce, Lavelle, Edgar, Mahoney, Hardcastle (Mansell, 69), Joel, Tanner, Cham (Wall, 65). Unused subs: Williams (GK), Edo, Platt.