Goals from winger Peter Halmosi, in the first half, and Sylvan Ebanks-Blake and Barry Hayles after the interval brought to an end three successive defeats for the West Countrymen.
Leicester, though, have not won in eight matches and will need to arrest that quickly if they are to remain in the Championship.
Neither side looked like creating a goal in the opening exchanges. The best chance of the game came from former Pilgrims loan player Jason Jarrett, whose pass back to goalkeeper Paul Henderson from midway inside his own half was over-struck.
After the sluggish start by both sides, Halmosi netted his second goal in successive games, after Hayles had controlled Gary Sawyer's long throw and teed up the Hungarian international midfielder.
Sawyer deserves credit, not only for the throw, but also a determined tackle which turned defence into an Argyle attack that led to the throw-in from which the Pilgrims scored.
Leicester's chances of getting back into the game disappeared within 14 minutes of the second half, when Ebanks-Blake chased down a long ball from the back, dispossessed Darren Kenton, forced an error from the defender and slid the ball home.
Argyle franked their superiority just after the hour when the impressive Ebanks-Blake latched on to Akos Buzsaky's throughball, rounded substitute Stephen Hughes and sent over the perfect cross for Hayles to dive in at the far post and convert.
Leicester then enjoyed their best patch of the game, with Argyle goalkeeper Luke McCormick twice saving from fit-again striker Matt Fryatt.
From the second of those, substitute Geoff Horsfield saw the ball deflect into his path but, with an open goal gaping, he ballooned the ball high over the crossbar.