The former Stevenage star carved out the home side's opening goal and then struck the winner as the plucky U's were brushed aside.
Boyd picked out prolific frontman Craig Mackail-Smith to break the deadlock in first-half stoppage time - the 14-goal striker clipping the ball over defender Johnnie Jackson before finishing smartly.
Colchester rallied and hauled themselves level in the 61st minute when former Posh striker Clive Platt netted on his return to London Road.
The big striker powered home a deep David Perkins cross with a close-range header - but Colchester's celebrations were cut short when Posh struck again moments later.
Boyd clinically fired into the bottom corner from 12 yards after goalkeeper Dean Gerken had kept out Gabby Zakuani's far-post header.