After arriving in Bucharest with a 3-1 lead from the first leg, Greece were able to stretch their advantage as Konstantinos Mitroglou netted in the 23rd minute on Tuesday.
The 25-year-old timed his run perfectly to reach a Vasilis Torosidis pass and finish low into the bottom corner from 15 yards for his third goal in the tie and fifth goal in qualifying overall.
Alexandros Tziolis' unfortunate own goal 10 minutes into the second half gave the hosts hope, but Fernando Santos' side were able to hold on and secure their passage to Brazil 2014.
The draw extends Greece's unbeaten run to eight matches and sees them qualify for consecutive World Cup finals for the first time.
Ciprian Tatarusanu - starting in the hosts’ goal in place of Bogdan Lobont - was called into action to deny Jose Holebas in the 17th minute but he could nothing about Mitroglou's opener five minutes later.
The Olympiacos forward broke the offside trap to collect a pass from Torosidis, and calmly fired home to extend Greece's aggregate lead.
Some neat build-up play ended with Ovidiu Hoban rolling a ball inside from the edge of the penalty area, and Torosidis' clearance struck Tziolis and looped into the top corner.
