Reid scored the only goal of the game after 51 minutes as Forest halted a five-game winless streak, but they were indebted to goalkeeper Lee Camp who made a couple of good saves to keep his team in front.
Forest also had chances to win by a bigger margin and might have done so had it not been for Posh keeper Robert Olejnik.
After finally kick-starting their npower Championship campaign last weekend with a 3-1 victory at Hull and following up those first three league points with a 2-0 success at Barnsley on Tuesday night, Peterborough were unchanged for the third straight game.
Forest made one change as Simon Cox was restored to the starting line up after a one-match suspension.
He partnered Billy Sharp up front as midfielder Henri Lansbury dropped out of the team and was absent from the squad ahead of the England Under-21s' forthcoming European Championship play-off double-header against Serbia.
Lewis McGugan looked up for it early on with three attempts on the Peterborough goal in the opening 10 minutes, although only one worked Olejnik and that was a 25-yarder straight at the Austrian.
Forest got the ball into the box regularly in the first 15 minutes but Chris Cohen twice failed to get enough on headers to worry Olejnik.
Peterborough won the first corner of the game after 17 minutes. It signalled the beginning of a sustained spell of pressure from the hosts during which Nathaniel Knight-Percival turned a shot over the crossbar.
Tyrone Barnett then curled an effort wide midway through the first half.
Forest battled back and McGugan had two further efforts either side of the half-hour mark - one going wide and the other being blocked - before a deflected Cox shot narrowly missed.
Camp was called into his first piece of meaningful action at the start of the second half.
Reid gave the ball away inside his own half and Michael Bostwick advanced to the edge of the area before forcing Camp to beat away his shot. From the resulting corner, Camp parried again from Barnett's header.
That got the Posh crowd behind their team but they were soon quietened by Reid's blockbuster.
After collecting the ball on the halfway line, the former Republic of Ireland international let rip from the left side of the area and his shot flew into the top corner of the net.
Camp immediately had to preserve Forest's lead with another parrying save to thwart Barnett after the striker managed to get his volley in after getting goal-side of Dan Harding.
Jermaine Jenas, on as a 61st-minute replacement for McGugan, thought he had scored his first Forest goal in almost 11 years midway through the second half but the on loan Tottenham midfielder was denied his moment of glory when a referee's assistant ruled that Sharp had run the ball out of play in the build up.
At the other end, Camp was at it again - this time getting down quickly to push a long-range effort wide from Posh sub Danny Swanson.
Jenas was denied again after 75 minutes when Olejnik got fingertips to his curler from inside the box. The Posh keeper then produced an even better save from the rebound to keep out Cox.
Peterborough put Forest under pressure during the closing stages but the visitors held on and would have done so by two goals to nil had Olejnik not blocked Sharp's shot in injury time.