The Pilgrims could have taken a seventh-minute lead when Sawyer flashed in a shot that whistled beyond the far post with David Marshall beaten.
But the Bluebirds hit back six minutes later when a Peter Whittingham corner was met by Mark Hudson. His goalbound header was destined for the roof of the net but Arglye keeper Romain Larrieu rose to tip over in spectacular style.
A Whittingham shot was pushed away by the overworked keeper with the onrushing Michael Chopra waiting to pounce.
Just after the half-hour mark, Marshall had to dive to his right to push away a shot from Alan Judge in a rare Argyle attack but the Bluebirds swiftly sent the ball downfield through Chris Burke and the Pilgrims were once again penned back in their own half.
Rory Fallon had been booked in the 29th minute after clashing with Anthony Gerrard and was later spoken to by referee Phil Gibbs following another challenge. Despite the crowd roaring for a red card after he floored Kevin McNaughton, the former Swansea striker remained on the field as the half-time whistle blew.
Two minutes after the restart, Jay Bothroyd twisted on the edge of the area but his shot flew over the crossbar. A minute later Chopra side-footed over after being released by Whittingham.
Ross McCormack replaced Chopra in the 71st minute as the Bluebirds went looking for the goal they desperately needed but when the score came it went to the visitors.
Totally against the run of play in the 84th minute a clearance by Paul Quinn was collected by Sawyer and his low shot went across Marshall went into the corner of the net.
In stoppage time, Joe Ledley was inches wide but it was a poor display from the Bluebirds after their two magnificent recent away victories.