Former United winger Anthony Elanga came back to haunt his former club with a stunning solo effort after just five minutes at the City Ground to earn all three points for Nuno Espirito Santo's side.
City have been reduced to battling for a place in next season's Champions League after a dismal campaign.
Manchester City overcame relegation-threatened Nottingham Forest 2-0 on Sunday to close to within one point of Premier League leaders Arsenal.
Former Liverpool defender Jamie Carragher has accused Nottingham Forest of lacking "class" after the club launched a blistering attack on referees chiefs following Sunday's Premier League defeat at Everton.
Ivan Toney will captain Brentford when he returns against Nottingham Forest on Saturday after an eight-month ban for breaching gambling regulations.
Wood left Newcastle to join Forest in a £15 million ($19 million) deal in June, but had scored only four times for his new club.
Bruno Fernandes completed a 3-2 comeback victory for Manchester United from the penalty spot after the hosts conceded twice inside the opening five minutes against Nottingham Forest in a rip-roaring Premier League clash at Old Trafford on Saturday.
Nottingham Forest have signed Swedish forward Anthony Elanga on a five-year deal from Manchester United, the two Premier League clubs announced on Tuesday.
Everton moved out of the Premier League relegation zone with a ruthless 5-1 win at Brighton on Monday, while Leicester's hopes of survival are hanging by a thread after a 5-3 defeat at Fulham.
Nottingham Forest have signed Ghana forward Andre Ayew until the end of the season, the Premier League club said on Thursday.
Marcus Rashford scored a dazzling solo goal as Manchester United beat Nottingham Forest 3-0 in the first leg of their League Cup semi-final on Wednesday to virtually book a place at Wembley next month.
A jury hearing inquests into the deaths of 96 Liverpool football fans in Britain's worst-ever sporting disaster at the Hillsborough football stadium in 1989 rules that they were unlawfully killed, with police failures to blame.
