The defeat piled more misery on Nottingham Forest, whose goal drought now stands at six Championship matches.
Boyd joined Forest on loan from Peterborough in March 2010 for the remainder of the season and helped the Reds to reach the Championship play-offs, where they lost to Blackpool in the semi-finals.
His move to the two-time European champions did not work out and he returned to Posh that summer.
Boyd’s strike after 20 minutes gave Peterborough successive league victories for only the second time this campaign and condemned struggling Forest to a fifth defeat in six matches.
Forest lost Paul Anderson to injury after just six minutes. He was replaced by Garath McCleary, who forced Posh goalkeeper Joe Lewis to tip a 20-yard effort round a post shortly after his introduction.
At the other end, Paul Taylor worked Lee Camp with a shot from outside the area.
However, there was nothing Camp could do to keep out Boyd’s superb curler from the right-hand side of the box.
The goal seemed to shake the home side’s confidence and Emile Sinclair went close before Taylor forced Camp into a superb save with a shot from the edge of the area after 37 minutes.
Taylor worked Camp again at the start of the second half before Forest came close to an equaliser when Tom Kennedy hacked a header by Marcus Tudgay off the line.
That seemed to encourage Forest and Lewis McGugan shot over the crossbar before the same played spurned a glorious chance to bring the Reds level.
McGugan was put through on goal by Dexter Blackstock but he lifted his effort over the advancing Lewis and the crossbar.
Taylor and then Tommy Lowe had chances to seal the points for Peterborough but both missed the target.
Posh were almost made to pay for those two misses when, with a minute remaining, substitute Andy Reid crossed the ball to McCleary and he powered his header straight at the chest of Lewis from close-range.
It meant Forest, who remain in the bottom three, had failed to score in their last six matches, the club’s worst run without a goal since the 2003-04 season.