The Iceland international midfielder, who had a loan spell with the Welsh club from Hoffenheim in 2012, was transferred to the Swans on Thursday as part of the deal which took Ben Davies and Michel Vorm to Tottenham.
In front of nearly 5,000 at Home Park on Sunday, the 24-year-old helped set up a goal for Jordi Amat and then netted twice himself having entered the friendly fray as a second-half substitute.
Northern Ireland Under-21 striker Rory Donnelly started up front in a Swans side that also included new signing Lukasz Fabianski in goal, while young midfielder Josh Sheehan was named in the line-up too.
Donnelly opened the scoring in the ninth minute when he pounced on a loose ball and saw his effort trickle over the line to the despair of Argyle goalkeeper Luke McCormick.
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