The decisive moment came through captain Morgan Gibbs-White, whose deflected strike proved enough to seal a 2-1 aggregate victory in the UEFA Europa League quarter-final.
Forest started brightly and took control when Porto were reduced to 10 men after an early red card. The breakthrough followed soon after, as Gibbs-White's effort took a heavy deflection and beat Diogo Costa.
Despite their advantage, Forest could not extend their lead. Nicolas Dominguez and others missed chances, while Chris Wood was forced off injured after a heavy challenge. Substitute Igor Jesus added energy but could not find the net.
Porto responded after the break and twice struck the woodwork, but Forest held firm under pressure to protect their narrow lead.
Manager Vitor Pereira praised his players' effort and spirit after the final whistle.
"I have a fantastic team, it's not about the manager," he said. "They have the spirit, character and quality. They deserve it. The club and the supporters deserve it."
He added: "We need to suffer together and feel proud at the end of a game - proud of the supporters and the result."
However, the victory came at a cost. Callum Hudson-Odoi, Murillo and Wood all picked up injuries, with Pereira admitting concern over Hudson-Odoi.
"Only Hudson-Odoi, maybe, is a muscular injury. We don't know yet," he said. "The other two, I think they will recover."
Forest will now face Aston Villa in an all-Premier League semi-final, but attention quickly turns back to survival in the Premier League, with a crucial clash against Burnley looming.
After a historic European night, Forest must now balance momentum with the reality of their relegation battle.
