Nani sent the Portuguese into a 31st-minute lead in Saint-Etienne, but Iceland were level early in the second period when Birkir Bjarnason fired home at the far post after Vieirinha was caught under the ball.
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It was Iceland that had the first chance of the match inside three minutes, but after breaking into the Portugal box, Swansea City midfielder Gylfi Sigurdsson could not beat Rui Patricio from close range.
Vieirinha was next to try his luck for Portugal in the 18th minute after breaking down the right, but the 30-year-old's strike was gathered by Iceland goalkeeper Hannes Halldorsson at the second time of asking.
Portugal's first outstanding chance of the match came in the 21st minute when Cristiano Ronaldo found the head of Nani with a cross from the left, but Halldorsson somehow made a point-blank save.
Ronaldo had a chance of his own less than two minutes later when Vieirinha delivered another telling cross from the right, but the Portugal skipper missed the target with a glancing header, before failing to connect on a sweeping Pepe pass.
Portugal continued to dominate as the first period developed, and the Iberian nation deservedly made the breakthrough in the 31st minute when Andre Gomes set up Nani, who fired home at the near post.
Iceland just could not stop the flow of pressure in the first 45 minutes and Ronaldo came close to meeting another cross from Vieirinha shortly before the break, but the first period came to an end with just one goal separating the two teams.
Ronaldo connected with a high ball early in the second period as Portugal looked to double their tally, but the 31-year-old's effort moved wide of Halldorsson's post.
Iceland were level in the 50th minute, however, when Bjarnason found himself unmarked inside the Portugal box and volleyed home a Johann Gudmundsson cross from close range.
The equaliser did not change the pattern of the match though as Portugal continued to look the more capable in the final third. Gomes showed super feet on the edge of the box just past the hour before curling one towards the bottom corner, but Halldorsson was on hand to make the save.
Portugal had another outstanding chance in the 71st minute when Nani met a free kick from Raphael Guerreiro, but the attacker's effort just missed the far post as Halldorsson was left rooted to the spot.
Halldorsson was then called into action in the 77th minute to keep out a deflected effort from Ricardo Quaresma, before Pepe headed a Gomes corner just over the crossbar five minutes later.
Ronaldo had an outstanding chance to score a second for Portugal in the 85th minute when Nani found his former Manchester United teammate with a cross from the right, but Ronaldo headed straight at Halldorsson.
Down the other end, Iceland had a rare chance when substitute Alfred Finnbogason found space inside the box, but the striker could only fire his effort straight at Patricio.
There was time for Ronaldo to strike two free kicks in second-half stoppage time, but both of the attacker's efforts hit the wall.
Next up for Portugal is a clash with Austria on Saturday evening, while Iceland will take on group leaders Hungary on the same day.