Argentinabeat Nigeria 2-1 in Tuesday's other Group D fixture thanks to a late Marcos Rojo victor, meaning La Albiceleste march into the round of 16 alongside Croatia and will face France in the next round.
Argentina took second place and will face France after beating Nigeria 2-1, a result that sent the third-placed African team packing. We have to be proud of that. Get live updates of Croatia vs Iceland FIFA World Cup 2018 Group D match here.
"We did everything we could, if you do that you can't be disappointed, we can look each other in the eye and can carry our heads high", said Iceland coach Heimir Hallgrimsson afterwards.
Needing a point to make certain of top spot, Croatia dominated early on, with Real Madrid pair Modric and Mateo Kovacic dictating the tempo without creating clear chances. "Denmark are strong. We need to play much better if we want to reach the quarter-finals. There was no percentage left on our batteries in the last minutes". Iceland presented themselves as a tidy, compact unit which proved hard for their opponents - led by the mercurial Luka Modric in midfield - were regularly frustrated as Iceland refused to relent, breaking forward themselves whenever they sensed that the Croatian defense was stretched.
The Iceland fans started the night's first "Thunder Clap" in support of midfielder Birkir Bjarnason, who briefly left the pitch with a bloodied nose after clashing with Marko Pjaca's elbow.
After a quiet opening with little action, Iceland started to gain control and apply pressure.
Five minutes before the break, Alfred Finnbogason played a one-two with Sigurdsson, but his shot from just inside the box went wide.
On the stroke of halftime, Aron Gunnarsson fired an angled shot that was bound for the top corner until Lovre Kalinic tipped it away.
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.
Iceland had to claim their first ever World Cup victory to have a chance of advancing and, urged on by fans chanting their famous Viking thunderclap, nearly equalised immediately.
Sverrir Ingason forced Kalinic to another spectacular save, seconds before his header shaved the top of the bar.
However, Lovren conceded a penalty soon after when he was adjudged to have handled the ball inside the area, with the spot kick subsequently dispatched by Gylfi Sigurdsson.