At Laugardalsvöllur Stadium in Keflavík, the home team scored the opening goal in the 21st minute, when Johann Gudmundsson's curved free-kick cross towards Turkey's back met with Ragnar Sigurdsson, who had the finishing header to lead Iceland 1-0 against Turkey.
Sigurdsson increased Iceland's lead to 2-0 in the 32nd minute with another header, this time a tap-in.
Turkey replied with a header goal of its own in the 40th minute, this time Dorukhan Tokoz scored to bring Turkey back into the contest.
It was Turkey's first loss in the group after three wins in a row.
Turkey has 9 points in 4 matches in Group H in Euro 2020 qualifiers.
On Saturday, Turkey defeated the defending world champions France for the first time in its history 2-0 to lead Group H in Euro 2020 qualifiers.
In their other group matches so far, Turkey defeated Albania 2-0 and beat Moldova 4-0.
Turkish national football team arrived in Keflavík International Airport on Sunday night. The Icelander officials kept the footballers in the airport about two hours at passport check station and rigorously searched their personal belongings.
Turkey issued a diplomatic note for Iceland to condemn the miss-treatment of Turkish footballers at the airport.
Before the match, Turkey’s Youth and Sports Minister Mehmet Muharrem Kasapoglu met with Iceland's Minister of Education, Science and Culture Lilja Dogg Alfreosdottir in Reykjavik.