The visitors took the lead in the second minute through Nikola Milenkovic but Rasmus Hojlund levelled. United were rocked again at the start of the second half by Gibbs-White, and Wood made it 3-1.
Bruno Fernandes struck a fine shot from just outside the box to give United hope just after the hour mark but it was not enough.
Ruben Amorim started his United reign last month with a draw followed by two wins, but predicted the club would “suffer for a long time” as he battled to improve their fortunes.
Reality is now starting to bite after a 2-0 defeat at Arsenal in midweek, followed by the Forest reverse at home.
Milenkovic left United goalkeeper Andre Onana rooted to the spot in the second minute, powering home a header from a corner – the third straight goal United had conceded from a corner.
The home side were level in the 18th minute after Forest goalkeeper Matz Sels could only parry Alejandro Garnacho’s shot and Hojlund steered home.
Forest made another lighting start to the second half when Gibbs-White let fly with a swerving shot from distance that beat Onana.
Forest extended their lead in the 54th minute when Wood took advantage of more uncertainty in the United defence to head home.
Fernandes pulled one back after patient play from Amad Diallo, who laid it off to the United captain, who whipped it into the back of the net.
The win lifts Forest to fifth on the Premier League table, but United are languishing in the 13th spot and Amorim is facing a huge task.
