Grayson: 'We were worthy winners.'
After a first half that was entertaining but neither side was able to take advantage, Preston moved into top gear in the second period.
Callum Robinson fired across the Dons' keeper Ian McLoughlin in the 66th minute for a well taken goal and then Joe Garner made sure of the victory with a close range header.
The win was Preston's fourth away win on the bounce.
Grayson said to reporters: 'It's a huge result for us. Obviously people will be playing it up because of where both teams are in the league and we knew the significance of it.
'We've come away with a real professional performance. I thought from start to finish we executed the game plan well because we knew that coming here we have to press and get all of the tactics right.
'Over the course of the game we were the worthy winners, that's for sure.'