Reet's fortunate 40th minute close-range finish from the Stags first chance of the match was rough on plucky Dale, who had dominated the first half.
But after the £25,000 former Sheffield Wednesday striker struck, the Stags took control to ease their relegation worries.
In a one-sided second half Reet might have had a hat-trick, while Gus Uhlenbeek, Stephen Dawson, Jake Buxton, Richie Barker, Gareth Jelleyman and Giles Coke also squandered gilt-edged chances.
Reet was given little chance to shine as Dale, prompted by the excellent John Doolan on his debut, took control from the kick-off.
Doolan, a former Mansfield star, marked his first start for Dale by controlling the midfield, creating two fine early chances. First Doolan set up Blair Sturrock, who wriggled clear in the area before crossing for Gary Jones to scissor-kick over the bar.
Then Doolan's superb pass allowed Alan Goodall to cross to the unmarked Sturrock, but with the goal gaping he hit the sidenetting.
For all their pressure and possession, Dale failed to force Stags' veteran keeper Kevin Pressman into a save throughout the whole match.
And they were made to pay when Reet struck against the run of play. Adam Rundle's poor corner sliced off the foot of Rickie Lambert and the unmarked Reet pounced from six yards.
Either side of half-time Reet then dragged three shots into the sidenetting as the home side grew in confidence.
Dale almost made them pay on a rare breakaway when yet another fine Doolan pass created the space for Lambert to cross to Sturrock, but he hammered wide.
From then on the Stags took control and should have had a hatful. Rory McArdle's diving header acrobatically cleared Buxton's powerful drive off the line, Coke fizzed a low shot across the face of goal and Uhlenbeek's dipping 30-yard volley landed on the roof of the net.
Then, in the final five minutes as Dale chased an equaliser, Dawson broke clear but fired wide, Jelleyman's shot was smothered by Matthew Gilks and Barker headed over at the far post.