Although fresh from back-to-back successes over promotion-chasing Sheffield United and Newcastle United, the Iron struggled to cope with Posh's pace and trailed to goals by Boyd and Craig Mackail-Smith at the halfway stage.
Boyd's seventh of the season broke the deadlock on 25 minutes, the wideman sending a superb left-footed half-volley well out of Joe Murphy's reach and into the bottom corner of the net.
Then, in first-half stoppage time, Jordan Spence failed to cut out a Lee Frecklington pass and Mackail-Smith stormed away unchallenged to place his shot wide of the stranded Murphy.
In between, Posh defender Tommy Rowe twice cleared in quick succession from his own goal-line, first hooking out a Paul Hayes shot before heading away Sam Togwell's effort.
Livewire Jonathan Forte had also gone close with a shot into the side-netting that partially demolished the goal!
Only Murphy's lightning reflexes denied Mackail-Smith a second seven minutes after the break, the Scunthorpe keeper dropping to save a close-range shot from Boyd's penetrating low left-wing cross.
Posh's Joe Lewis had to be rescued by the woodwork at the other end when a mistake by Gaby Zakuani let in Forte to send an overhead kick against the crossbar.
There could have been further home goals, Mackail-Smith hit a post and Aaron McLean lifted a shot a foot too high before Boyd finished off Scunthorpe by steering a 77th-minute penalty to the left of Murphy after Michael O'Connor had needlessly brought down Charlie Lee.
Referee Mick Jones, demoted to the Championship after the infamous beach ball incident a week earlier, raised a few chuckles when delaying kick-off while Scunthorpe skipper Rob Jones burst a large blue balloon that had blown on to the London Road pitch.