Former Swan Rory Fallon was in a Plymouth side skippered by Wales international Carl Fletcher.
With only 48 seconds on the clock, Nathan Dyer raced through the middle but his shot was blocked by Pilgrims keeper Romain Larrieu.
Joe Allen seized on the rebound but his goalbound drive was headed clear.
It was all one-way as the visitors were penned in their own half and Angel Rangel fired into the side netting in the eighth minute.
The Swans were almost caught out on the half hour when Dorus de Vries dropped a cross but Shane Lowry's angled lob landed on top of the netting.
A free-kick by Federico Bessone just before the interval whistled over the visitors crossbar but the opening period ended with the Swans gaining all the possession but unable to turn it into goals.
Paulo Sousa made a double change for the second half with Gorka Pintado and Trundle replacing Allen and the ineffective Idrizaj.
The deadlock was broken in the 51st minute with a near-post strike from Trundle.
Dyer started the move before slipping a pass out wide to Pintado, whose low cross was met by Swansea's talisman for a clinical finish.
Plymouth should have levelled in the 63rd minute when Fallon met a cross from Alan Judge but his close range header was turned round the post by de Vries.
Pintado had the ball in the net in the 73rd minute but was rightly flagged for being in an offside position.
The elusive Dyer continued to cause problems for the visitors as Swansea pressed hard for the second goal that would surely seal victory.
Trundle created space but tried one trick too many as he waited for help to arrive up front.
In time added on, Shane Lowry received a second yellow card after tangling with Pintado to leave the Pilgrims facing the final few minutes with ten men.