Milan Badelj hit a sweet half-volley for his side early in the second half, and Ivan Perisic struck in a 90th-minute victor for Croatia after Gylfi Sigurdsson had pulled Iceland level from the penalty spot.
Iceland's first World Cup adventure came to a valiant end on June 26 as they were beaten 2-1 by Group D winners Croatia due to a late strike from Ivan Perisic, with Argentina qualifying as runners-up instead. Gylfi Sigurdsson levelled with a penalty but Ivan Perisic grabbed a last-gasp victor.
The victory for Zlatko Dalic's Vatreni means that Croatia finish top of the standings and will face Denmark in the last 16.
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. The midfielder was more accurate two minutes later as he thundered a volley into the back of the net to open the scoring.
Defender Sverrir Ingason twice threatened for Iceland, hitting the crossbar with a header in the second half.
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The match was evenly poised in the final 10 minutes of the first half, but chances were few and far between for both nations.
Iceland pushed forward, and threw men forward in search of a victor which looked increasingly like it would send them through.
Never before had Croatia won their final group-stage game at the World Cup, having lost in 1998, 2002 and 2014 and drawn in 2006.
"We want to beat Iceland to stay top of our group".
Hallgrimsson cut his teeth in global management as assistant to Swede Lars Lagerback, who steered Iceland to the Euro 2016 finals, where they beat England in the last 16 but fell to host nation France at the quarter-final stage. Iceland's maiden World Cup campaign, meanwhile, has ended with a first-round departure.
For all of Croatia's possessional dominance Dalic's charges offered little going forward in the first half and it was Iceland who grew into the game.