McManus headed home Barry Robson's free-kick to secure all three points against the Pilgrims, for who Alan Judge missed a penalty just before half-time.
Franks rounded things off when Boro broke from a corner that had seen Argyle goalkeeper David Stockdale go up and Franks slotted into an unguarded net.
Argyle went close after Chris Clark engineered a breakaway from Jamie Mackie, whose low cross was turned just past the post by David Wheater. Reda Johnson headed Judge's subsequent corner wide.
Boro took advantage of some slack marking in the Argyle box to open the scoring midway through the first half after the Home Park visitors had won a free-kick on the right.
McManus was allowed far too much time and space to rise and nod home an in-swinging delivery from his captain Robson.
The Pilgrims spurned the opportunity to get back into the game just before half-time when Judge's shot from just outside the area was handled by Justin Hoyte and referee Scott Mathieson awarded a penalty.
Judge, who had scored three previous times from the spot this season, stepped up, but found Brad Jones impassable as the Australian goalkeeper saved low to his right.
Boro were able to hold Argyle at arm's length after the interval, with two Mackie efforts - one low and wide and one slashed well off target - the only time they were put under pressure.
Stockdale kept the Pilgrims in the game, saving well from Robson's powerful drive, before Boro substitute Scott McDonald should have finish off Argyle but failed to get anything on Lee Miller's cross from just a few yards.
Argyle head coach Paul Mariner tried hard to spice up his side with some imaginative substitutions but to no avail.