Croatia had the upper hand in the opening 20 minutes but the home team dealt with the pressure comfortably before establishing their own more direct passing game as the half went on.
Iceland were then hit by a double blow when forward Kolbeinn Sigthorsson went off injured just before half-time and Olafur Skulason received a straight red card five minutes into the second period.
Skulason was dismissed for tangling with Ivan Perisic when the Croatian was through on goal.
Iceland coach Lars Lagerback praised the bravery of his team but was less than complimentary about Spanish referee Alberto Undiano.
"The players did a fantastic job but the referee didn't have his best day," Lagerback told RUV television. "I'm not satisfied.
"Someone watched the replay on TV and they said it (the red card) was very, very questionable, but it wasn't just that. In many situations the referee didn't know if he should blow or not.
"To defend for almost 45 minutes with one less man on the pitch ... I can't describe in words what these players have done," added Lagerback.
Croatia went close early on through Luka Modric but Sigthorsson and strike partner Alfred Finnbogason also spurned excellent chances for Iceland in the first 10 minutes.
Eidur Gudjohnsen came on to replace the injured Sigthorsson up front but the former Barcelona and Chelsea striker then had to drop into midfield when Skulason was sent off.
Croatia's second-half passing was mesmerising at times and Iceland, roared on by a sell-out crowd, had to throw themselves into a series of challenges to thwart their more skilful opponents.
Perisic was always in the thick of the action for Croatia and came close to breaking the deadlock when his shot flashed just wide in the 83rd minute.
"I am not happy with the result because we should have been able to score after having an extra man for 40 minutes," said coach Niko Kovac. "We resorted to playing long balls for too long.
"I expected us to keep it on the ground more and we just didn't implement the game plan. We didn't use the width of the pitch enough, we failed to create space in midfield but I am convinced we will get it right in the return game."
The sides meet again in the second leg in Zagreb on Tuesday to determine who goes through to the World Cup finals in Brazil in June.
THE MATCH IN A TWEET
- Sports & Recreation
- Kolbeinn Sigthorsson