The Light Blues, already confirmed as champions of the Scottish third tier, were quickest off the starting blocks, registering chances against the Pars in the first few minutes.
Rangers kept up the pressure midway through the first half, but the Pars defence was able to thwart chances by Aird and Mohsni, while an effort by Dean Shiels on the half-hour mark, following a whipped ball by Steven Smith, scraped just past the post.
At the beginning of the second half, the Light Blues took the lead through Shiels, the attacking midfielder pouncing on a loose ball after Nicky Law saw his initial effort saved.
In the 71st minute, however, the Pars equalised thanks to Lewis Martin, the young defender catching out the Gers' defence following a corner.
The away side strove to go back into the lead, and nearly did so in the 79th minute when Shiels cut the ball back to Black outside the box, his shot cannoning off a defender up onto the post and going wide.
Once the final whistle was blown, Rangers celebrated going the entire season unbeaten and, with their ascension to the Scottish Championship, getting a step closer to the Scottish Premiership where Old Firm rivals Celtic await once again.