Conor Washington and Joel Lynch scored early in the second half for Rangers to end their six-match losing run.
Wins for fellow-strugglers Birmingham and Blackburn left Forest one place above the drop zone, ahead of Rovers on goal difference only.
It means the East Midlands club, who are at home to Ipswich next weekend, will go down if they fail to at least match Blackburn's result - Rovers are away to Brentford.
Nottingham Forest keeper Jordon Smith produced a fantastic double save to deny Rangers early on.
Jordon Smith dived low to his left to stop Pawel Wszolek's shot and when Washington directed the loose ball towards Matt Smith, the Rangers striker saw his header clawed away.
Alex Smithies also produced a fine save at the other end, tipping over an effort from the dangerous Mustapha Carayol, but Jordon Smith was the busier keeper during a tense first half, also gathering shots from Massimo Luongo and Ryan Manning.
However, he was unable to rescue Forest after Joe Worrall's indecisive challenge let in Washington four minutes into the second period.
Luongo played the ball forward and Washington wriggled away from Joe Worrall before firing beyond Smith for his first goal in 11 appearances.
Lynch then scored his third goal of the season against his former club to double Rangers' lead on the hour mark.
When Luke Freeman's right-wing corner was cleared as far as Manning, the Irish youngster sent the ball back into the penalty area and Lynch headed home from close range.
Forest responded with a spell of sustained pressure in which they very nearly pulled a goal back.
After Worrall's header from Ben Osborn's corner was cleared off the line by Manning, the ball eventually broke to Jamie Ward, whose shot was fumbled by Smithies before the R's keeper managed to complete the save.
Matty Cash then missed a great chance for the visitors, shooting wastefully wide of the near post after being set up by Ward's clever pass.
Smithies, Rangers' player of the season, atoned for some uncharacteristically uncertain moments with a stunning late save to deny Cash.
Again Ward was the provider pulling the ball back for Cash, whose first-time strike was pushed away at point-blank range.
Additional reporting by the Press Association.