The home side started brightly and nearly took the lead in the first minute, but a great challenge from Boro captain Adam Jackson denied Albertt Rusnak.
Marcos Lopes was next to try his luck on 11 minutes but his shot went well wide of the target.
City broke the deadlock after 18 minutes when John Guidetti found himself in space down the left-hand side. His cross was met by George Glendon, who headed powerfully into the net.
Just two minutes later Swedish striker Guidetti, who was excellent all night, tried an audacious flick with his back to goal but his effort went wide. However, Boro were struggling to stem the City tide and went further behind on 23 minutes.
Sinan Bytyqi picked the ball up on the left wing and cut inside before unleashing a shot from just inside the area that Leutwiler could only get his fingertips too.
Half-time: Manchester City U21s 2 Boro U21s 0
The second half started in very much the same vein and City nearly scored a third after 47 minutes. Burn conceded a free-kick when bringing down Guidetti on the edge of the box. From the resulting set piece Bytyqi smashed the ball against the crossbar.
On 50 minutes Boro shocked the home side by pulling a goal back through Mark Kitching. A ball through the middle was flicked on by Curtis Main and the U18 captain burst between Dedryck Boyata and Shay Facey to coolly slot the ball past Ian Lawlor in the City goal.
Any thoughts of a comeback were short lived as City scored their third after 56 minutes. Leutwiler did well to keep out a Rusnak shot but Guidetti was on hand to fire the ball home.
Boro tried to hit back again and on 61 minutes Andy Halliday stung the goalkeeper's hands from range with a fiercely-struck shot.
Boro's tormentor-in-chief Guidetti hit the bar again before he was substituted, as he makes his way back from injury.
On 72 minutes Boro thought they had strong grounds for a penalty as City keeper Lawlor wiped out Halliday when attempting to clear, but only a corner kick was given.
The scoring was completed on 82 minutes when City sub Jordy Hiwula rounded Leutwiler before slotting into an empty net.
A young Boro side never gave up but greater experience showed in the home team and in Guidetti they had a genuine cutting edge who has scored goals in senior football with Feyenoord in recent seasons.
Manchester City: Lawlor, Drury, Leigh, Facey, Boyata, Huws (Fofana 76), Lopes (Capt) (Pozo La Rosa 64), Glendon, Guidetti (Hiwula 69), Rusnak, Bytyqi. Unused subs: Johannsen (GK), Cole.
Boro: Leutwiler, Bennett, Burn, Jackson (Capt), Meling, Bradley Halliday (Waters 46), Jones, Kitching (Park 69), Main, Williams, Andy Halliday (Kneeshaw 80). Unused subs: Coddington (GK), Weledji.
Boro MoM: Mark Kitching. Looked solid and composed in only his third U21 game which was capped off with an impressive run and finish for his goal.