Brazilian midfielder Taddei stunned the home crowd in the 73rd minute but Raul gave Real a lifeline when he notched home a controversial strike two minutes later.
Substitute Mirko Vucinic killed off Los Merengues' hopes in stoppage time to cap a great night for Luciano Spalletti's man.
Roma were the better team throughout the game, keeping Iker Casillas busy with continued raids.
On the other hand, Real missed the presence of prolific striker Ruud van Nistelrooy, who missed the game through injury.
Real had the first chance after 16 minutes when Julio Baptista's deflected free-kick was palmed away by Roma keeper Alexander Doni.
Two minutes later, Real had to thank goalkeeper Casillas for keeping the score goalless.
Alberto Aquilani's powerful bullet from 30 yards cannoned off the crossbar.
Few moments later, the talented midfielder gathered the ball again after being fed by Francesco Totti before hitting a low shot that brought a superb save from Casillas.
In the 21st minute, Baptista should have done better when he chested Robinho's chip pass inside the area but he fired poorly wide.
The Beast was unlucky to see his curling free-kick strike the crossbar four minutes after the interval.
The woodwork came to Real's rescue once again six minutes past the hour mark when it denied Vucinic's cracking first-timer from inside the area.
Taddei broke the deadlock in the 73rd minute when he capitalized on Gabriel Heinze's dreadful marking to connect with Max Tonetto's pinpoint cross and head home.
Raul equalized two minutes later when he controlled Robinho's through pass inside the area before firing a low shot home.
However, Television replays showed that the Real skipper was in an offside position.
Real's hopes suffered a major blow when defender Pepe picked up a second yellow card 19 minutes from time.
Vucinic sealed Roma's precious victory in stoppage time with another header after being set-up by Christian Panucci's right-wing cross.
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