The midfielder, who returned to the club last week having spent six months on loan in 2012, came off the bench to net twice in the final 18 minutes to round off a comprehensive win
The Iceland international, who rejoined Swansea from Tottenham earlier this week, came off the bench midway through the second half at Home Park to round off a comfortable victory for the Premier League outfit.
Swansea failed to win either of their games on a recent mini-tour of the United States, but had far too much for League Two outfit on their return to home shores.
Unsurprisingly, Garry Monk's side controlled proceedings from the off and it took them just nine minutes to open the scoring.
Northern Irish striker Rory Donnelly was on hand to put Swansea ahead as he pounced on a spill from Plymouth goalkeeper Luke McCormick.
Jonjo Shelvey and Wayne Routledge both went close to doubling the visitors' lead, before Plymouth's Carl McHugh forced new Swansea stopper Lukasz Fabianski into a fine save.
Jefferson Montero - another recent arrival - made his bow for Swansea in the second half, but it was Jordi Amat who grabbed the second goal 21 minutes from time.
Sigurdsson, introduced just three minutes earlier, provided the corner for Amat's goal, and the 24-year-old took centre stage when firing home Alex Bray's cut-back soon after.
And the midfielder was not finished there, as he curled home a superb free-kick in injury time to complete a comprehensive Swansea win.