Tschumeni-Nimely’s shot grazed the Reds' crossbar shortly after the restart.
Adnan Januzaj missed a great chance to give United the lead midway through the second period but fired high over the bar from Tyler Blackett’s left wing cross.
Dunn then looked certain to find the net for City in the 70th minute, only to see his fierce drive bravely headed away by Keane.
Jesse Lingard, fresh from his heroics on the first-team’s summer tour, took centre stage again 15 minutes from time, when he scored from the penalty spot after being felled in the City area by Ashley Smith Brown.
And United almost increased the lead shortly afterwards when Larnell Cole unleashed a screamer that crashed against the post.
In the end, Lingard and Petrucci's strikes were enough to keep City at bay and earn Warren Joyce's men yet another piece of silverware.
United: Johnstone, Wootton, Thorpe, M Keane, Vermijl (Blackett 42), Cole, Ekangamene, Petrucci (Pearson 81), Lingard, Januzaj, Macheda (Lawrence 51)
Subs not used: Gollini, Rothwell