It gave the Copnor club a quick-fire double over the Oilmen having beaten them away just 48 hours earlier.
Nathan Paxton gave the tired hosts a lift by opening the scoring after only 11 minutes.
Fawley equalised at the start of the second half but within a minute Paxton struck again.
Soon afterwards the striker notched his third goal to put Moneyfields in charge.
Ryan Pennery added a fourth late on.
It’s been a good run for Moneys with three wins in quick succession as they are finishing a tough season in a positive manner.
Manager Dave Carter praised his side.
He said: ‘I can’t ask for anymore from the players than nine points in four days.’
Tomorrow, Fareham Town and Horndean continue their end-of-season marathons with home games against Folland Sports and Hamworthy United, respectively.
The Reds, who have played seven games already this month, are in action another three times this week.
Manager Steve Stone has a day of meetings at Wembley Stadium so he has put Howard Dove in the hotseat.
Stone, however, hopes to race back in time to take charge for the second half.
The home side have been hit by the departure of defender Sean Howe to work in America.
‘We are back to playing every two days again,’ said Stone.
Horndean manager Craig Pearce is expecting a tough test from Hamworthy United at Five Heads Park (7.45pm).
His side go into the game in confident mood after thumping Bournemouth Poppies 6-1 at the weekend.
‘We played Hamworthy at their place recently and came away with a narrow win,’ said Pearce.
‘They caused us a few problems so we know they can be a threat going forward.
‘We will have to make sure we defend properly and then hopefully our attacking quality will see us through.
‘It is a game we need to win if we are serious about achieving a top-six finish.
‘We have a lot of aching bodies at the moment but must look to go again.’
Horndean play again on Thursday night when they entertain Team Solent.