The Scottish international striker headed home a right-wing cross from forward partner Cameron Jerome ten minutes before the interval to seal the Welsh side's victory.
There had been a question mark over Thompson's selection before the game, with the former Dundee United and Rangers man having failed to find the target in six previous outings, but manager Dave Jones found his loyalty rewarded.
Cardiff's margin of victory should have been greater against a Plymouth side who have now scored once in their last five matches.
After Argyle forward Micky Evans fired wide in the second minute following Vincent Pericard's low near-post cross, the Pilgrims found chances few and far between against a defence well marshaled by recalled Dutchman Glenn Loovens.
Cardiff hit the bar when midfielder Ricardo Scimeca's shot deflected off Lilian Nalis before skimming the crossbar, before Jerome incredibly missed a golden opportunity three yards in front of an unguarded goal.
At the other end, Pericard was inches away from opening the scoring with a lunge at Paul Connolly's dangerous cross, before Cameron made amends for his earlier gaffe by setting up Thompson for the winner.
Argyle threw the kitchen sink at Cardiff in the opening stages of the second half, but the nearest they came to breaking the deadlock was when French midfielder Nalis headed Tony Capaldi's inswinging corner delivery narrowly over Neil Alexander's crossbar.
They also won an indirect free-kick just inside the penalty area after Loovens had passed back to Alexander, but Pilgrims skipper Paul Wotton was unable to celebrate his 400th first-team appearance with a trademark free-kick goal.
Cardiff nearly caught Argyle on the break when the impressive Jason Koumas played Jerome in, but the teenage striker was this time denied by a spectacular flying save from Argyle goalkeeper Romain Larrieu.