Oboavwoduo and Whittingham had struck to send City in 2-0 to the good at the break.
Dickson then extended his fine goal scoring form in the FA Youth Cup straight after the restart before Oboavwoduo struck twice more to seal the deal and his own treble.
Ben Wilkinson’s youngsters were deserved and impressive winners, carving out a host of opportunities to go alongside those five goals.
But City were also indebted to goalkeeper George Murray-Jones who produced a superb spot kick save to deny Sam Glenfield when Fleetwood were awarded a penalty with score still only 1-0 in our favour.
Our reward for victory is a quarter-final tie at the Academy Stadium in early March where we will play host to either Oxford United or Leeds United.
Wilkinson’s side were seeking to instantly bounce back from the disappointment of last Saturday’s Premier League Under-18 Cup quarter-final exit to Spurs.
And the City youngsters made the ideal start, powering into a fifth-minute lead thanks to a sweet strike from Oboavwoduo.
Joel Ndala was the initial architect, driving at the Fleetwood defence from the left flank before finding Isaiah Dada Mascoll on the edge of the box.
His crisp first-time pass found first Dickson and then Nico O’Reilly who instinctively teed up the advancing Oboavwoduo who drilled a low first time shot home past visiting keeper Rio Cragg.
Cragg was called upon again on 19 minutes, diving to parry away a 20-yard goal-bound effort from O’Reilly after a superb mazy run from the City midfielder.
Next it was Joel Ndala’s turn to be thwarted by the Fleetwood keeper, Cragg leaping to his right to keep out a low drive.
Ndala did have the ball in the net just before the half-hour, curling home a delightful effort, but the strike was cancelled out with the City winger adjudged to be offside.
Then it was Dickson’s turn to be frustrated, Cragg racing out to block his shot after we had breached the Fleetwood back line once again.
However, the visitors were then handed a potential route back into the game on 33 minutes when Tom Galvez challenged Billy Jones in the box with referee Richard Aspinall pointing to the spot.
Sam Glenfield stepped up to take the spot-kick, but City keeper Murray-Jones was equal to the task, producing a superb save to keep the penalty out.
And City made the visitors pay for that missed opportunity as we finally doubled our lead three minutes later through Whittingham
Ndala was the provider, threading an exquisite ball into the path of the onrushing Whittingham and the City midfielder showed great skill to thread a superb shot into the far corner of the net.
Whittingham and Ndala combined again straight after the restart with Cragg tipping a stinging Ndala effort just around the post.
City weren’t to be denied for long however with a third arriving on 50 minutes through Dickson as he kept up his record of scoring in every round.
The striker latched onto a pinpoint Oboavwoduo cross to fire home from eight yards with the Fleetwood defence at sixes and sevens.
Cragg was centre stage once more on the hour to deny O’Reilly before Ndala saw a fierce shot smack back off the post - but Oboavwoduo was there to follow up and claim his deserved second goal and our fourth in total.
And the winger then sealed a superb night's work by heading in on off the bar five minutes from time as City rounded off a fine victory in style.
How we lined up
George Murray-Jones was in goal shielded by a back four of Jacob Wright, Layle Samuel, Jadel Katongo and Tom Galvez.
Isaiah Dada Mascoll was the holding midfielder with Justin Oboavwoduo, Nico O’Reilly in the engine room.
The front three was made up of Matty Whittingham, Will Dickson and Joel Ndala.
CITY XI: Murray Jones, Wright, Samuel, Katongo, Galvez, Dada Mascoll (Harrison 60), Oboavwoduo, O’Reilly (Okeke 78), Whittingham, Dickson (Alpha Ruprecht 71), Ndala
Subs: Noble, Grant, Muir.
FLEETWOOD: Cragg, Jones, Arthur (Richmond 60), Khela, Johnson, Hughes, King, Morrison, Lane (Marsh 73), Glenfield, Brown
Subs: Hand, Belliza, Butterworth, Kearns, Roberts
What it means
City’s reward for victory over Fleetwood is a quarter-final tie at home to either Oxford United or Leeds United.
They meet on Wednesday night at the Kassam Stadium for the right to play City.
Quarter-final ties are due to take place by Saturday March 4 with a confirmed date and kick-off time to be confirmed in due course on mancity.com.
City are back in Premier League Under 18 North action on Saturday.
We play host to Middlesbrough at the CFA where we will be looking to maintain our place at the top of the table.
Kick-off is scheduled for 12pm (UK).