After holding the well-organised visitors to 0-0 at half time, Latvia caved in during the second half, conceding goals in the 66th, 77th and 90th minutes as Iceland dominated possession.
In the other matches in Latvia's group the Netherlands beat Kazakhstan 3-1 at home while the Czech Republic scored an important away win, beating Turkey 2-1.
Latvia's next game, at home against Turkey, kicks off 19:45 Riga time on Monday October 13.
