The Toffees will now face the winners of the match between Real Madrid and Los Angeles Galaxy.
They made an encouraging start, with some slick passing and movement causing problems for the Bianconeri, who also set up in their usual 3-5-2 system.
Jagielka had the ball in the net in the sixth minute, flicking Steven Pienaar's in-swinging free kick beyond Marco Storari. However, the linesman quickly raised his flag for offside and replays showed his decision to be correct.
Juventus struggled to get into the game in the first half and could have found themselves trailing by half time had Stones's header not ricocheted off the upright.
Everton eventually took the lead on the hour mark thanks to a solo effort from Kevin Mirallas, who had also done little to affect proceedings up until that point. Darron Gibson spotted the run down the right, and the Belgian winger cut inside his marker before tucking the ball past Marco Storari.
Juventus began to stir after the goal and should have equalised when Mauricio Isla's low ball into the box presented Federico Peluso an opportunity to score, but Stones got back to block his shot superbly.
The game was now end-to-end action, with Pienaar charging down the ball and leaving himself with just Storari to beat, but his side-footed shot missed the target.
It took a brilliant strike to finally breach the Blues' defence, who failed to deal with a ball in from the right. Leon Osman allowed the ball to run across him and Kwadwo Asamoah carried on to smash a left-footed shot across Tim Howard and into the top corner.
That is the way it stayed until the full-time whistle, thereby instigating penalties.
Osman was first up, but he saw his kick saved by Storari. Every player after him found the back of the net until Andrea Pirlo stepped up to take his spot kick that would have seen Juventus win the match. In uncharacteristic fashion, the Italian blazed wide.
Everton's victory was sealed when Tim Howard beat away Peluso's penalty after John Stones and Seamus Coleman had slotted home their respective spot kicks.