Stafford took a shock early lead through David McNiven, but goals from Louis Soares and John Grant put Aldershot in front before Chris Flynn drew the visitors level.
Jonny Dixon gave Aldershot the lead just before half-time and veteran Neil Grayson thought he had rescued a point for Stafford, but Davies fired home with 14 minutes left to seal a sixth consecutive league win for Aldershot.
The home side pressed for an early goal but with seven minutes gone, McNiven produced a fine finish from 18 yards that gave Stafford a shock lead.
However, that lead lasted barely two minutes as Grant played the ball into Soares in the area and his left-foot shot nestled into the top-left corner.
Ten minutes later Grant went from provider to scorer when he received a pass from Dixon and fired in from the edge of the area.
Stafford came roaring back and were level after 34 minutes when substitute Sebastian Arnolin set-up Flynn and his precise effort beat Nikki Bull.
Just as it looked like Stafford might reach half-time level, Soares' corner was flicked on by Ben Harding and Dixon was on hand to head home.
The visitors battled well in the second half to restrict Aldershot to long-range efforts and with 66 minutes gone they were level in spectacular fashion when veteran Grayson produced a magnificent lob from 25 yards that gave Bull no chance.
For all their battling Stafford could not hold on and with 14 minutes left substitute Davies, who had only been on the field for four minutes, curled in a free-kick from 20 yards to put Aldershot back in front.
Late on McNiven saw a shot flash wide as Stafford failed to find a way back into the game.
Source: http://www.thisisstaffordshire.co.uk/