Wylde, a free signing from St Mirren, opened the scoring after 40 minutes before Carey, who joined from Ross County, bagged his first Pilgrims goal four minutes after half-time to seal the win.
The Dons started brightly, winning four corners in the opening six minutes, and new signing Andy Barcham had two early chances.
But Wylde had the best effort of the early stages with James Shea forced to push away his shot for a corner.
Former Rangers winger Wylde then opened the scoring five minutes before the break with a close-range volley from Jake Jervis’ cross from the right flank.
Argyle doubled their lead after 49 minutes as Carey hit a stunning shot from outside the penalty area which flew beyond Shea’s dive.
Plymouth’s biggest scares came when Carl McHugh was forced to clear off the line from Adebayo Akinfenwa and Jake Reeves fired over from the edge of the box.