Sean O'Driscoll came closest to opening the scoring in a goalless first half through Simon Cox, who had a half-volley saved brilliantly by Posh keeper Robert Olejnik.
Boro threatened through Michael Bostwick, who had a deflected drive saved by Lee Camp.
Forest continued to press and got their reward early in the second half, when Reid launched an unstoppable drive from distance to score the only goal of the game.
Posh pushed forward in the closing stages, but it was Forest who nearly doubled their advantage minutes from time when Radoslaw Majewski hit the post with a header from close range.
An important win for Forest sends them into the top half of the table, while a disappointing home defeat for Boro leaves Darren Ferguson's side rooted to the foot of the Championship.