The former Stevenage winger handsomely repaid another chunk of his £260,000 January transfer fee as Posh sank County with two goals in a five-minute burst early in the second half.
Producing some excellent close passing football on a difficult surface, Posh had the better of the opening half and even without top scorer Aaron Maclean, who is out for the rest of the season with a knee injury, they should have had more to show for their entertaining build-ups.
County's Sean Deeney was easily the busiest 'keeper denying Peter Gain before going full stretch to his left to push Craig Mackail-Smith's low drive behind for a corner.
Josh Low fired over and Deeney also had a let-off after racing yards out of his goal. He failed to reach the ball and watched with some relief as Mackail-Smith's 30-yard shot went just the wrong side of a post.
Also lacking a key marksman with Jason Lee suspended, along with defenders Alan White and Ian Ross, County went close when Posh's Mark Tyler saved a Lawrie Dudfield shot with his legs. And they should have taken the lead three minutes before the break after Dudfield's run on the left produced a pass that left Junior Mendes in the clear, only for the much travelled front man to fire alarmingly wide.
Boyd took control on 50 minutes, forcing the ball into the net after his fierce initial shot had squirmed out of Deeney's grasp. Then he turned provider heading back a Low corner for Welsh international defender Craig Morgan to head his first goal for the club.
County boss Steve Thompson rang the changes for the last 20 minutes and one of his substitutes Tcham N'Toya almost brought a life line. The Congo striker's fierce volley from 15 yards brought a superb reflex save from the otherwise little troubled Tyler.