Dons boss Mark McGhee shuffled his pack following the midweek Scottish Cup defeat, with goalkeeper Jamie Langfield, Sone Aluko and Jerel Ifil dropping out.
Hibs fans were furious not to receive a penalty when Danny Galbraith was barged to the ground by Jerel Ifil but Calderwood did not think his side had a strong claim.
But it was Tade, who scored the winner when the sides met back in February, who gave his side the lead when he tapped home after Mole capitalised on a Jerel Ifil error.
And, although Aberdeen made the brighter start, it was the visitors who could have taken an early lead when Enoch Showunmi outmuscled Jerel Ifil, but goalkeeper Jamie Langfield gathered at the feet of the former Leeds striker.