However, their dominance from start to finish, which began with Luka Modric scoring from the penalty spot in the 13th minute, was a tad surprising.
It was 2-0 in the 19th minute when Kalinic used his heel to turn in Ivan Strinic's low cross.
Greece struggled to regain composure and rarely attacked, but Sokratis Papastathopoulos briefly silenced the home crowd, sending a header over keeper Danijel Subasic and into the net.
However, relief for the visitors was short lived.
But just three minutes later Croatia restored their lead as Sime Vrsaljko found Perisic with a cross to the back post, and the Inter Milan winger headed home.
The fourth goal came four minutes after the break from Andrej Kramaric, swooping in after another Greek error, by Kostas Stafylidis.
Goalkeeper Orestis Karnezis was shown a yellow card for bringing down Kalinic, as the Real Madrid midfielder made no mistake in the first leg qualifier.
"We had a tremendous game".
"We must root out any complacency immediately and head to Greece as if the score was 0-0", Croatia coach Zlatko Dalic told Croatian broadcaster HRT. "But it's not over". Italy, however, is known to play the most important matches on the highest level, so we still have them as a favorite in this match. "We had a lapse in concentration and conceded a goal, but I can't really complain". Just three minutes later, Croatia again reached a two goal advantage. Now one who has seen the Greek national side do close to the impossible over the years might say that it's not over, but it was hard not to be impressed with the Croats, who also boast a significantly better squad.
While it's clear that Switzerland, Italy, and Croatia are a cut above the rest out of these eight teams, all of the teams have their qualities of course. However, they are going against Denmark who had a much better performance in a tougher group.
With 10 European spots already filled by group winners and Russian Federation, the remaining 8 teams with best second place scores from groups will face off for the remaining spots in the World Qualifiers.