The second half offered more attacking chances with Boyce and Burke going close for their respective sides but it was the replacements who made the difference.
On the hour, Derry boss Tiernan Lynch threw on Paul McMullan and Danny Mullen, and four minutes later the pair combined to open the scoring with Mullen latching onto McMullan's looping cross to fire past McGinty in the Rovers goal.
The lead did not last for long as 16-year-old Noonan - who came on just before the opening goal - headed home the equaliser.
An ambitious effort for Roberto Lopes from 35 yards was tipped onto the crossbar by Maher in the Derry goal but it fell straight to teenager Noonan.
Stephen Bradley's men upped the tempo and came close to taking the lead when Josh Honahan weaved his way around multiple red and white shirts before sending an effort narrowly wide.
Adam Matthews then made a crucial block to deflect Duffy's strong strike to safety, to the relief of the travelling fans.
However, the goals weren't done though as with just two minutes of normal time left the away side took the lead with McEneff converting Danny Mandroiu's from close range to secure the three points for Shamrock Rovers against his former side.