Zlatko Dalic's men comfortably continued the containment job that had started in the 50th minute of Thursday's fixture in Zagreb, when they opened up a three-goal cushion.
Greece coach Michael Skibbe made six changes in the hope of sparking a special comeback in Piraeus, but his side offered next to no attacking threat in a mundane encounter. A disallowed goal in the 79th minute was as good as they could muster.
Croatia maintained their unbeaten record in play-off matches and Dalic will hope that getting his country to the finals is enough to win him the job long-term.
Though a throaty roar greeted the first whistle, the home side's lack of invention soon muted the crowd and off-target long-range efforts from Anastasios Bakasetas and Sokratis Papastathopoulos were all Greece had to show for a soporific first half.
Captain Vasilis Torosidis did his best to bring some entertainment, entering a long-running row with Nikola Kalinic.
Goalkeeper Danijel Subasic was not called into action until the 41st minute when he nipped Zeca's flick-on off the head of Kostas Mitroglou, but the visitors served a reminder of their attacking threat by marching up to the other end, Ivan Perisic clattering the post with a rifled left-footer from 30 yards.
Mitroglou drove wide just before the hour, but Greece could not alter the pattern of play in the second half as Croatia's defence continued to pick off their opponents' ceaseless wayward passing.
Substitute Dimitrios Pelkas had the ball in the net 11 minutes from time, but Torosidis was clearly offside in the build-up.
A game that produced just one shot on target - a deflected Panagiotis Tachtsidis effort from the edge of the box three minutes from time - did little to lift spirits, but it will have been cheered throughout Croatia, as they now look to better group-stage eliminations in their past three World Cup appearances.
