Kwadwo Asamoah's thumping effort for Juve with 10 minutes remaining cancelled out Kevin Mirallas' counter-attacking strike had put Everton ahead on 61 minutes.
The game went straight to penalties after 90 minutes, with Leon Osman missing his spot-kick, before Andrea Pirlo did likewise for the Italian side.
Everton goalkeeper Tim Howard then saved from Federico Peluso in sudden-death to give Roberto Martinez' side a 6-5 spot-kick success.
Earlier, Martinez's team had an early Steven Pienaar free-kick disallowed, while John Stones hit the goal-frame with a header just before half-time.
The Italian champions included Carlos Tevez following his summer signing from Manchester City, and he played 83 minutes for his new side.