Abbi Grant's first goal for Scotland earned the national side their second win from two games in the Pinatar Cup.
Grant capped an impressive display against Iceland when she broke free inside the box before arrowing a shot high into the net.
The Scots had to be patient in Spain as a dominant first-half display failed to yield a goal.
Erin Cuthbert almost doubled Scotland's lead against opponents who rarely threatened.
Scotland spurned a number of chances to add to their lead after the break, with Caroline Weir and Emma Mitchell both going close.
Following a 3-0 victory against Ukraine, Shelley Kerr's side secured their second win with a bit to spare.
The Pinatar Cup acts as a warm-up for Scotland's return to competitive action next month in Cyprus in a Euro 2021 qualifier, having opened Group E with victories over Cyprus and Albania.
The Scots face Northern Ireland on Tuesday in their final match in the cup.
Scotland goalscorer Abbi Grant: "It was my first start for Scotland so to get a goal was the icing on the cake. I feel like the first chance had was probably the easiest but I was happy to hit the net in the end.
"For my goal, I just saw the chance open up for me and thought I would just have a go. To score for Scotland was a special feeling."