The Reds had to better Blackburn Rovers' result at Brentford to beat the drop, but their dramatic demolition of the Tractor Boys made events elsewhere inconsequential.
Mick McCarthy's men had the better of the early possession, but a nervy Forest almost took the lead just after the half-hour mark when Britt Assombalonga's cross was volleyed over in front of goal by Eric Lichaj.
Ipswich's best opportunity of the first half came moments later as Dominic Samuel gained possession in the box and shot on the turn, Jordan Smith producing a reaction save to push the ball against the crossbar.
Mark Warburton's side took the lead from the penalty spot against the run of play when Bartosz Bialkowski brought down Jamie Ward in the box, allowing Assombalonga to step up and rifle the ball into the top corner, sending the home fans into a frenzy of relief and elation.
Forest came out for the second half like a side rejuvenated, and they took a major step towards survival in the 57th minute as captain Chris Cohen's 25-yard screamer beat Bialkowski with the aid of a deflection.
The Reds grew in confidence as the half progressed and had the chance to add a third from the penalty spot when Ward drew a foul from substitute Joshua Emmanuel.
Assombalonga stepped up once again, only to be denied by an impressive save from Bialkowski, who guessed correctly and turned the ball over with a strong hand.
However, Assombalonga soon made amends for his error, powering through the Ipswich defence in the 69th minute before rifling a powerful strike into the roof of the net to turn a day which began with relegation nerves into one of celebration for Forest.
Forest's final-day victory, coupled with Birmingham City's win at Bristol City condemned Blackburn to relegation, despite Rovers overcoming Brentford 3-1 at Griffin Park.