Croatia had their first clear chance when Badelj's missile crashed onto the bar six minutes into the second half.
Milan Badelj, moments after hitting the bar, scored the opening goal in the 53rd minute.
Having already qualified the 1998 World Cup third place side would only not top the group if Nigeria were to beat Argentina and overturn the five goal difference between the two sides, so a 3-0 win, and Croatia lost to Iceland.
Iceland could have finished second in the group with a victory because Argentina beat Nigeria 2-1 at the same time.
While most eyes were on Argentina and their do-or-die match with Nigeria in Saint Petersburg, Croatia wrapped up top spot in Group D in Rostov-on-Don thanks to a slick second-half volley by Milan Badelj and a late strike by Ivan Perisic, sandwiching a penalty equaliser by Gylfi Sigurdsson.
Iceland have been eliminated from the World Cup after a 2-1 defeat against Croatia in their final Group D game.
Midway through the period it was the Nordic side, who had beaten Croatia in qualifying for Russian Federation, who took control, threatening from set-pieces and interceptions.
"We've played Croatia four times in four years, we've often said we're like a married couple - we're trying to get divorced, but we always meet up again", the Iceland coach said at a recent media conference.
Iceland faced a huge task as Nigeria nearly simultaneously equalised against Argentina, but they reacted swiftly.
Iceland were rewarded in the 76th minute when second-half substitute Dejan Lovren handled the ball and Sigurdsson rifled the resulting penalty into the roof of the net. As for Croatia, it has a round of 16 date against Denmark on Sunday. But Ivan Perisic punished a defensive error to make it 2-1 at 90 minutes.
The World Cup match between Iceland and Croatia will be broadcast live on FS1.
The Iceland defender Sverrir Ingason almost scored twice just moments later, heading just over and then again off the crossbar.
"We did not look the best on the pitch today, but it's important to win on such occasions", said Perisic.