A 3-0 victory in Wednesday's home first leg did the damage, despite Allan Smith's 72nd-minute effort, as the Wasps clinched back-to-back promotions.
Dunfermline were hoping for a repeat of their semi-final heroics against Forfar in which they came back from a 3-1 deficit to win 6-1 in the second leg and triumph 7-4 on aggregate, but it was not to be as they also finished with 10 men after Stephen Husband's dismissal.
Relegation to the Second Division for the first time since 1986 caps a miserable season for the Pars, who were docked 15 points at the start of April having gone into administration while they remain the subject of a transfer embargo.
The hosts were expected to come firing out of the blocks in a bid to turn around their heavy first-leg defeat but it was Alloa who looked more likely to add to their three-goal advantage - Graeme Holmes, Stephen Simmons and Kevin Cawley missing the target.
Cawley then forced goalkeeper Michal Hrivnak to tip his effort around a post as the Pars struggled to create any first-half openings.
Hrivnak was at it again to deny Cawley just minutes after the restart while Calum Elliot twice fired off-target either side of a similar effort from Dunfermline's Andrew Geggan.
Josh Falkingham finally tested Alloa goalkeeper Scott Bain in the 71st minute before Smith found the net for Dunfermline 60 seconds later with a right-footed finish from close range.
Any hopes of a dramatic comeback were extinguished when Husband saw red for serious foul play in the 85th minute.
Although the hosts did lay siege to Bain's goal in the closing minutes, forcing the stopper into two fine saves.