A raft of young players looking to impress before the club head out to the United States for a tour were brought on, two of which got on the scoresheet.
Arsene Wenger's side knew nothing other than victory would do after defeat by Dinamo Zagreb in Croatia in their opening game - and with two meetings with group favourites Bayern Munich still to come.
Erik ten Hag's side, beaten 3-0 at home to Bournemouth in the Premier League on Saturday, needed to beat the Bundesliga champions and hope that there was no winner in theother group game between Copenhagen and Galatasaray.
City's Bernardo Silva - whose Portugal side went out at the last-16 stage - made his first pre-season appearance, but the Blues are still without 15 other players who were on duty in Russia.
Forest had possession when the game was stopped but the game restarted with the ball at the feet of Liverpool goalkeeper Caoimhin Kelleher and the away side kept the ball, went down theother end and eventually found the winner.
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In a tight and cagey second leg, Gabriel Martinelli had Arsenal's best chance ofthe first half but shot straight at Manuel Neuer after Jamal Musiala had forced David Raya into a full-stretch save at theother end.
In the ninth minute of added time, Bellingham headed across for Dani Carvajal to poke in the winner. The dramatic late victory helped Real leapfrog Girona and move two points clear at the top of La Liga.
The drama then switched to theother end in eight added minutes as Declan Rice's deflected shot gave Arsenal the lead before substitute Gabriel Jesus raced clear to wrap up the win as the stadium exploded in elation.