Defender Chambers struck with the aid of a slight deflection two minutes into the second half to ensure Billy Davies' side leapfrogged Leeds into fifth place in the table.
Forest, who have won six of their last seven league games, are still unbeaten at the City Ground this season and sit just a point behind an automatic promotion spot with a game in hand on their rivals.
City, chasing their first league win in four games, have not won away from home since early November and remain six points above the bottom three.
Forest, for whom Robert Earnshaw replaced Paul Anderson due to a hamstring strain, were denied by David James in the sixth minute.
Earnshaw clipped a 25-yard free-kick towards the bottom corner and the former England goalkeeper was forced into a sprawling save.
James was on his toes again in the 17th minute, keeping out Forest striker Marcus Tudgay's goalbound shot from outside the penalty area at full stretch.
City striker Brett Pitman headed the visitors' first chance straight at Forest goalkeeper Lee Camp a minute later, but neither side could work a clearcut opening until Albert Adomah threatened again for City 10 minutes before the break.
Louis Carey crossed and Adomah headed over the crossbar from a central position 12 yards out with only Camp to beat and the game remained goalless at half-time.
Chambers did well to block City striker Dave Clarkson's shot from outside the penalty area shortly after the restart and then popped up at the other end to give Forest a 47th-minute lead.
Forest midfielder Chris Cohen delivered a superb cross from the right into the area and Chambers despatched a 12-yard shot, with the aid of a slight deflection, into James' bottom-left corner.
City were almost back on level terms five minutes later when Camp pulled off a fine save to turn away Adomah's thunderbolt from 25 yards.
The visitors were giving as good as they got despite being a goal down and Jamal Campbell-Ryce was next to go close when his 25-yard shot fizzed the wrong side of Camp's post and Adomah wasted a golden chance soon after when blazing over the crossbar from the right side of the area.
Forest finished strongly as Earnshaw fired in a 30-yard drive that James held on to and Lewis McGugan flashed an angled drive just over the crossbar, but Chambers' fourth goal in eight matches was enough to secure all three points.