It had looked like Lewis McGugan's 88th-minute penalty would salvage a draw for Forest but Chambers deflected Jem Karacan's early cross past Lee Camp, who then went on to save a penalty from Shane Long.
Ian Harte put Reading ahead but a Kris Boyd penalty and a goal from Robert Earnshaw turned the game on its head.
Karacan and Jimmy Kebe restored the Royals' lead before McGugan levelled from the penalty spot shortly before Chambers' unfortunate intervention.
Guy Moussi went straight back into the Forest side on his return from injury, replacing the suspended Chris Cohen in midfield.
Garath McCleary came in for the injured Paul Anderson while Earnshaw was recalled at the expense of Marcus Tudgay..
Mathieu Manset made his first start for Reading in one of two changes made by Royals boss Brian McDermott. The Frenchman replaced Steve Howard, while Mikele Leigertwood started ahead of Jay Tabb.
Long looked lively early on, setting up a couple of half-chances for Manset and forcing Camp into a routine save before winning the free-kick from which Reading took the lead.
The Republic of Ireland international had his heels clipped by Chris Gunter as he chased the ball on the left side of the area after 19 minutes.
Harte shot over the Forest wall and into the far top corner. Camp got a touch but could not keep it out.
Another Harte free-kick almost brought a second goal for the Royals just after the half-hour mark but his inswinging cross was headed over the crossbar by Manset.
Forest equalised seven minutes before the break when Lewis McGugan turned Leigertwood inside the area and fell over the midfielder's leg.
The referee took advice from his assistant before pointing to the spot and Boyd blasted the penalty into the bottom left corner.
Reading, after being in control for so much of the first half, were suddenly hanging on as Alex McCarthy did well to push away McCleary's swerving shot.
At the other end, Camp had to tip another free-kick from Harte over the crossbar on the stroke of half-time.
Harte continued to cause Forest problems early in the second half as Manset looped a header inches wide from the Irishman's cross.
However, the hosts went ahead in the 51st-minute when Earnshaw was allowed to drift inside the box before sending a shot across McCarthy that went in off the inside of the far post.
But the lead was shortlived as Karacan equalised three minutes later. The midfielder met Harte's corner 15 yards out and his header sailed over Camp and underneath the crossbar.
Reading almost edged ahead again on two occasions either side of the hour mark.
Kebe latched on to Leigertwood's long pass before lobbing the advancing Camp but his effort bounced wide of the open goal.
Camp then pushed away another shot from Kebe following great linked up play between the Malian and Manset.
However, Kebe was not to be denied for a third time in quick succession.
Jobi McAnuff's corner broke to Zurab Khizanishvili whose shot was blocked, but Kebe tucked in the rebound from six yards out.
Forest thought they had salvaged a point when substitute Hal Robson-Kanu brought down Gunter and McGugan converted the resulting penalty. However, Chambers turned the ball past Camp.
That was still not the end as an amazing game climaxed with a penalty save from Camp after Chambers had handled.