Darren Carter fired the hosts ahead in the 35th minute with a 25-yard strike but Paul Anderson levelled with a superb effort five minutes after the restart and defender Chambers prodded home the winner from close range.
Brown returned to management on Thursday when he penned an 18-month contract at Deepdale and was tasked with saving the Championship strugglers from relegation.
The 51-year-old had been out of work since leaving Hull last year and his immediate aim will be to inspire an upturn in fortunes at the division's bottom club.
North End are seven points adrift of safety after a disastrous campaign which saw Darren Ferguson axed after less than a year in charge.
Staying in the Championship remains the overriding priority for the famous old Lancashire outfit, but their first-half performance offered cause for optimism.
They were vibrant from the outset against a Forest side managed by ex-Preston boss Billy Davies and who harbour ambitions of winning promotion this season.
In the third minute, Preston threatened when Danny Mayor crossed dangerously and Chris Brown saw his 12-yard header fly wide.
Two minutes later, Forest orchestrated their first meaningful attack when David McGoldrick saw his 12-yard shot flash just wife of Andy Lonergan's goal.
North End were then dealt a blow in the 15th minute when striker Brown succumbed to injury and was replaced by Paul Hayes.
Three minutes later Forest threatened again when McGoldrick fired goalwards from 18 yards but his effort drew a save from Lonergan.
The pendulum swung back in Preston's favour in the 26th minute when an inswinging corner from Keith Treacy was greeted with a firm header from Craig Morgan.
The ball flashed just wide and Hayes then saw a 12-yard shot comfortably saved by Forest stopper Lee Camp.
Moments later Preston led when Carter found the net with a superb left-footed strike which flew into the bottom left corner from 25 yards.
Forest striker Robert Earnshaw warmed Lonergan's hands from 20 yards in the 40th minute but five minutes after the restart the visitors were level.
McGoldrick found Anderson and he embarked on a fine run from halfway and a sweet left-footed finish from 12 yards.
Preston sought to respond strongly but midfielder Barry Nicholson volleyed over the crossbar and Forest began to regain control.
Chris Gunter fired just wide from 12 yards and Earnshaw also threatened before Forest claimed victory in the closing stages when Chambers prodded home from six yards after an inswinging corner from Lewis McGugan fell to him.