It was a first win in six Championship matches for the Pilgrims, who had four of their five January signings in the starting line-up, while head coach Ian Foster could also celebrate his first league success since taking charge a fortnight ago.
Cardiff had taken an early lead and were in control for the opening half-an-hour before Hardie equalised in the 31st minute when he opened his body to slot a low cross from debutant Alfie Devine into the net.
Argyle did not look back after that as Hardie netted for a second time in the 52nd minute and then provided the cross from which Morgan Whittaker made it 3-1 in the closing stages with his 16th goal of his outstanding season.
Whittaker, the subject of much transfer speculation already this month, was the Argyle captain with Joe Edwards and Jordan Houghton both named among the substitutes.
Foster made three changes to the starting line-up from the 1-1 draw away to Huddersfield Town, with new recruits Devine and Adam Forshaw both making their debuts, and there was also a call-up for Mickel Miller.
Forshaw was picked to play in central midfield ahead of Houghton and Adam Randell just 24 hours after his signing from Championship rivals Norwich City.
There were home debuts for Ashley Phillips and Darko Gyabi after both made their first Argyle appearances against Huddersfield, while Matty Sorinola, a free-agent addition to the squad on Wednesday, was on the bench.
Miller lined-up at left wing-back in a 3-4-2-1 formation, with Bali Mumba on the right and the pair of Forshaw and Gyabi in between them.
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