It took just four minutes for them to edge in front as Kean Bryan crossed low from the left of the penalty area. Boro’s defence failed to clear and Sinan Bytyqi followed up to smash home from close range.
A few minutes later Bryan just cleared the bar from a 20-yard free-kick as City looked for a quick second, but Boro were having none of it and settled into the game. Mark Kitching had a low shot blocked before the home side equalised from the penalty spot.
With 20 minutes played Luke Armstrong was brought down by Angus Gunn and England U17 international Priestley Griffiths sent the goalkeeper the wrong way.
City’s lead was restored eight minutes from half-time when James Horsfield sent over a delicious cross from the right and Jack Byrne showed great awareness to tuck in from close range.
Just 90 seconds later it was almost three when Bytyqi shot on the turn inside the penalty and struck a post.
City’s wide players, especially Dominic McHale, gave Boro’s full-backs a hard time and it was no surprise when the visitors went further ahead after 58 minutes when McHale worked his way into the Boro box on the right and curled a low shot past Joe Fryer.
Kitching brought a relatively comfortable save from Gunn before substitute Scott McCarthy wasted a good chance to reduce the arrears when heading over.
There was time for another goal and that went to City as, with 84 minutes played, Byrne delivered a free kick from close to the right-hand edge of the penalty area and Mathias Bossaerts rose higher than anyone to knock onto the head of Bersant Celina and into the net.
This result leaves the Blues very much in contention to qualify for the knockout stages of the competition ahead of their final game of Phase 2 against Aston Villa on Saturday.