Mackail-Smith swooped to head Peterborough's 62nd-minute opener, powering home a far-post header from Grant McCann's free-kick from the right touchline.
Mackail-Smith doubled his tally in the 75th minute with a scorching right-foot half-volley from close range after latching on to a crossfield ball from Tommy Rowe.
Posh striker Aaron McLean made it 3-0 when he headed home skipper Grant McCann's corner from the right two minutes later as Argyle folded in the Devon sun.
Earlier in the second half Mackail-Smith came close to scoring when he brilliantly brought the ball down out of the air with his right foot and then volleyed just wide with his left following a defence splitting pass from full back Seth Ofori-Twusami.
Argyle's best chances fell to recalled winger Craig Noone, who fired just over from 18 yards in the 27th minute following a mazy run. Noone also had a far-post header from Dean Parrett's left-wing corner well saved by visiting keeper Joe Lewis just after Mackail-Smith's opener.