The Magpies played well within themselves, but still ruthlessly disposed of their opponents as first-half goals from recalled striker Andrew Carroll and Wayne Routledge within eight minutes of each other effectively settled the fate of both sides.
However, Argyle should have taken the lead before the leaders had had time to settle.
Leading scorer Jamie Mackie was set up by Damien Johnson's cut-back on the right edge of the area, but was denied by Toon goalkeeper Steve Harper.
From Alan Judge's corner, Newcastle allowed centre-back Bondz N'gala a free header, and although the West Ham loan player met it on the full, he could not direct it on target.
The Pilgrims were made to pay for that profligacy midway through the half when Carroll, who had previously wasted a good opportunity when set up by Danny Guthrie, put Newcastle ahead.
Guthrie was again the provider, from a corner, as Carroll beat Reda Johnson with ease to send a looping header past goalkeeper David Stockdale and inside his left-hand post.
Eight minutes later, Routledge raced on to a perfect through-ball from Joey Barton to outpace Zimbabwean international full-back Onismor Bhasera and slot home from an acute angle.
To their credit, Argyle responded positively, with Mackie, Bradley Wright-Phillips and Judge all going close with long-range shots before half-time, and Judge rattled Harper's crossbar with a dipping shot after the break.
Newcastle reasserted their authority late on as the Pilgrims chased a consolation goal, and substitute Leon Best smashed a shot against the crossbar.
By and large, though, Newcastle were content to play containing football, and the near 2,500-strong Toon Army's started celebrating their return to the Premier League after a one-season stay in the Championship.