North End midfielder 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 npower 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.
Carter found the net with a superb left-footed strike which flew into the bottom left corner from 25 yards but Anderson levelled when he embarked on a fine run from halfway and a sweet left-footed finish from 12 yards.
Forest claimed victory in the closing stages when Chambers prodded home from six yards after an inswinging corner from Lewis McGugan fell to him.