Appleton is the bookies' favourite to be installed as Blackpool boss following Ian Holloway's switch to Crystal Palace.
And if this was his Portsmouth swansong, his year in charge ended in a fourth straight defeat in all competitions.
The Bees took just nine minutes to take the lead. Donaldson met Adam Forshaw's free-kick from the left with a superb flicked header that left Pompey keeper Simon Eastwood with no chance.
The hosts' best chance of the first half came a minute before the break when Izale McLeod latched on to Lubomir Michalik's searching ball over the top, however, he lashed his effort just wide.
Free kicks from Akos Buzsaky and substitute Liam Walker were Portsmouth's best attempts at finding an equaliser as the Bees held on comfortably.