Aston Villa's Morgan Rogers bagged a double as the visitors twice came from behind to win 3-2 at West Ham United to remain in the thick of the Premier League title race on Sunday.
Igor Jesus slotted through a crowd two minutes from time to clinch a first away victory in Europe for Forest since 1995.
Villa moved into second place, three points behind Arsenal who suffered only their second league loss of the season.
Villa are on a run of 10 wins in 12 matches in all competitions after a five-match winless run to start the Premier League season.
Elsewhere, Celtic suffered a humbling 3-1 defeat by Midtjylland, and Real Betis won 2-0 at home against Olympique Lyonnais with first-half goals from Abde Ezzalzouli and Antony.
Matty Cash's first-half goal fired Aston Villa to a 1-0 victory over Manchester City on Sunday, as the club celebrated Unai Emery's third anniversary as manager with a memorable win.
Forest, who sacked Ange Postecoglou after just 40 days and eight games in charge on Saturday, had not won in 10 games stretching back to the opening weekend of the Premier League season.
Newcastle got a worrying glimpse of life without Alexander Isak as they were held to a 0-0 draw in their Premier League opener at Aston Villa despite Ezri Konsa's dismissal.
Manchester City's Matheus Nunes scored deep in injury time to salvage a crucial 2-1 Premier League victory over Aston Villa on Tuesday in their breathless chase for a Champions League berth next season.
Forest, who sacked Ange Postecoglou after just 40 days and eight games in charge on Saturday, had not won in 10 games stretching back to the opening weekend of the Premier League season.
Newcastle got a worrying glimpse of life without Alexander Isak as they were held to a 0-0 draw in their Premier League opener at Aston Villa despite Ezri Konsa's dismissal.
Manchester City's Matheus Nunes scored deep in injury time to salvage a crucial 2-1 Premier League victory over Aston Villa on Tuesday in their breathless chase for a Champions League berth next season.
Manchester City manager Pep Guardiola has called on fans to treat their Premier League match against Aston Villa at the Etihad Stadium on Tuesday as a "final" as his side chase qualification for next season's Champions League.
With Prince William watching on, Villa defender Ezri Konsa did a facepalm gesture as he and teammate Youri Tielemans tried to contain their laughter, while PSG's Fabian Ruiz and Ousmane Dembele exchanged puzzled glances.
Paris St Germain kept alive their dream of a first Champions League title on Tuesday by squeezing past Aston Villa 5-4 on aggregate after a thrilling second leg of their quarter-final which the English side won 3-2.
Unai Emery says his players can feed off the energy of their fans as Aston Villa seek to overturn a 3-1 deficit in Tuesday's Champions League quarter-final second leg against Paris Saint-Germain.
Aston Villa must make home advantage count and draw energy from their supporters in the return leg of their Champions League quarter-final against Paris St Germain at Villa Park on Tuesday, manager Unai Emery said.
The Argentine international, dubbed a 'specialist in provocation' by French sports daily L'Equipe, was seen wearing a hat that celebrated the Albicelestes' success while covering up a French cockerel emblem on Tuesday.
Morgan Rogers gave Villa the lead at the Parc des Princes, but the French champions levelled through Doue before half-time. Kvaratskhelia put PSG ahead early in the second half and Mendes added a late third.