Golden boy Boyd bagged a brace as Darren Ferguson's men climbed into third position after making hard work of shaking off the side propping up the League One standings.
Crewe provided an unexpected early twist by getting in front and later ensured another bout of nail-biting inside London Road when notching a second half leveller.
In fact the Railwaymen needed only two minutes to break the deadlock courtesy of frontman Tom Pope who steered a low shot through the legs of Posh keeper Joe Lewis.
That setback was clearly a shock to the Posh system and it took the home side until the second period to find a reply.
Boyd hauled them level with a fierce 50th minute finish after makeshift central defender Charlie Lee had charged into the box - and only three minutes later the turnaround was completed when Aaron McLean collected a slick pass from strike partner Craig Mackail-Smith and coolly tucked away his 12th goal of the season.
But Posh certainly hadn't banked on Pope pulling the visitors level moments later.
The big forward was picked out by a decent Danny Shelley delivery and left Lewis with no chance when finding the net with a classy glancing header at the near post.
Mackail-Smith failed to capitalise in a one-on-one situation before Chris Whelpdale steered a golden headed chance straight at Crewe keeper Stuart Tomlinson.
But an unlikely source was soon on hand to restore the Posh advantage. Midfield tiger Dean Keates chose the perfect time to register his first goal of the season when rifling an unstoppable thunderbolt into the roof of the net after 69 minutes.
Boyd then added some flattering final gloss to the scoreline when guiding a sublime low finish into the far corner three minutes from time.