Juve went ahead when Alvaro Morata slotted in against his old club after Carlos Tevez's effort was spilled.
Real levelled when Cristiano Ronaldo nodded in James Rodriguez's cross.
But the holders looked out of sorts and slipped behind again as Dani Carvajal tripped Tevez after the break and the Argentine dispatched the spot-kick.
Juventus manager Massimiliano Allegri signalled he was content with the scoreline as he brought on central defender Andrea Bazagli just after the hour and his side shut down the contest, limiting Real to a clutch of half chances.
Whether Juve's advantage is enough to survive the return leg at the Bernabeu is yet to be seen, but it was a result to relish for the noisy home support as captain Gianluigi Buffon led the celebrations at the final whistle.
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