The fit-again centre-forward cancelled out Conor Wilkinson's opener just before half time to spark a much improved second half display from his side that featured goals for fellow 2011 FA Youth Cup winners Jesse Lingard (2) and Tom Thorpe.
The Reds struggled as the rain fell in the first half and almost went behind to a Jan Gregus free-kick that clipped the bar. In front of the watching David Moyes, Bolton were awarded a penalty in the 20th minute when Ben Amos rushed from his goal to up-end Tom Youngs. The keeper atoned with a superb save, diving to his left to thwart Youngs from the spot.
Warren Joyce's side finally started to carve out some noteworthy chances with Tom Lawrence lashing over after an exchange of passes with Lingard and Adnan Januzaj blasting off target from long range. Cole, who displayed some neat skill at times, played a one-two with Lawrence but could only scuff his finish wide.
However, the visitors drew first blood when Cole was dispossessed and Tom Youngs raced past Guillermo Varela to set up Wilkinson and the ex-Millwall man stepped inside Michael Keane to bury a left-footed drive past Amos.
It stung United into a response as Januzaj was denied by Jay Lynch at the near post from a Tyler Blackett pass. From Januzaj's corner, Will Keane was on hand to level after Cole's wayward shot crashed against Lingard and fell kindly for him, the hitman chesting down and thumping home.
Despite Bolton feeling the goal was offside, MUTV replays proved otherwise and it was just the tonic as the second half started with the hosts