Jerel Ifil picked up Aberdeen's fifth red card in five matches after he aimed kick at the Greece international.
Saint Johnstone's opener came after Dons defender Jerel Ifil had conceded a cheap corner kick out on the left.
Aberdeen's reshuffled line-up also had Lee Miller alone up front, with Andrew Considine, Jerel Ifil midfielder Gary McDonald called in.
Dons boss Mark McGhee shuffled his pack following the midweek Scottish Cup defeat, with goalkeeper Jamie Langfield, Sone Aluko and Jerel Ifil dropping out.
IFIL, a large shareholder, had threatened to withdraw its support.
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.
The car company (30%-owned by the Agnellis) is creating an Internet portal, selling everything produced not just by Fiat, but also by the various industrial and financial interests of the Agnellis' separate conglomerate, Ifil.
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.
Ifil was sent in for an early bath in the 55th minute after the Englishman followed through on an aerial challenge with Samaras and delivered a kick at the Greek's thigh that was spotted by the stand-side assistant referee.
Paton and Steven MacLean did their best to hold the ball up when they received it in forward positions, but too often they found themselves lacking in midfield support and suffering from nervy distribution by defenders Ifil and Zander Diamond.
Rooney outmuscled Ifil as the ball bounced back towards the Aberdeen goal but, with the goal at his mercy, the striker contrived to blast the ball wide of the near post when a shot across the bows of Howard seemed the better option.
This may eventually lead to a merger of Ifil with Fiat, opening the door to an outside investor being brought in to rescue the Fiat Auto division, which is labouring under a heavy dependence on the Italian market, a lack of scale and earlier diversification into difficult emerging markets such as Brazil.
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