Despite dominating 120 minutes of play in rain and swirling wind, Serbia could not find the breakthrough goal.
And after nine penalties each, it was Nemanja Maksimovic who hit home the winning penalty to give the Europeans a 6-5 win in the shootout and a chance to progress to the final.
In Wellington, Senegal booked a final-four spot after pipping Uzbekistan 1-0.
Mamadou Thiam's strike was enough to earn Senegal a semi-final showdown against Brazil in Christchurch.
