A revamped but businesslike Croatia topped their World Cup group as Ivan Perisic's 90th-minute goal helped them maintain their ideal record with a 2-1 win on Tuesday that also ended Iceland's qualification hopes. Iceland drew against Argentina in their other Group D match.
Everton's Sigurdsson tested Lovre Kalinic from a free-kick, while Birkir Bjarnason, who suffered a nosebleed early on, had shots blocked in quick succession.
But as Iceland strained for the victor and a berth in the last 16 it was Croatia who threatened, free-kicks by Perisic and Rakitic worrying Halldorsson.
Croatia looked more energetic at the start of the second spell and almost took the lead in the match in the 51st minute but Milan Badelj's rocket from outside the box crashed against the crossbar.
Croatia have won three consecutive World Cup matches for the first time.
Sverrir Ingason forced Kalinic to another spectacular save, seconds before his header shaved the top of the bar.
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On 73 minutes Bjarnason fluffed a close-range opportunity but Iceland's lifeline arrived a minute later when Dejan Lovren handled a cross by Sigurdsson in the penalty area.
A 76th minute penalty from Gylfi Sigurdsson, cooly dispatched into the roof of the net as if a riposte to the crucial spot kick miss against Nigeria last Friday, looked to have secured a point for Iceland before Perisic's late strike sucked any remaining wind from the Icelandic sails. Iceland's maiden World Cup campaign, meanwhile, has ended with a first-round departure.
Croatia have no such issues, coasting to a 2-0 victory over Nigeria before stunning 2014 World Cup runners-up Argentina, and their fluid, attacking football has made them one of the most attractive sides in the competition.
Croatia midfielder Mateo Kovacic completed 78 of his 79 passes attempted in this game (98.7%); the best percentage of any player to start the match.
He did the dirty work too, won half of his duels (7/14) and both of his tackles as well as recovering the ball more than anyone else on the pitch.