Dougie Fife scored the game's only try, in the first half, and it proved to be the difference as Greig Laidlaw and Ian Madigan each kicked two penalties for their respective sides.
The win moved Edinburgh into the top half of the RaboDirect PRO12 and Du Preez, who followed head coach Alan Solomons to Scotland this summer, insists they can maintain this form.
"It's very good for us to beat them as it just shows how much we've come on as a team recently," he said. "Winning is a habit, so long as we keep improving.
"It's been really easy for me to settle in - the guys have been great, but I knew all the systems before I arrived so that was a big help to me.
"But it's not about me. We've got a good squad of guys all pushing each other for places, so it's great to be in the team. I just try to do my best every week."
Edinburgh's next challenge is back-to-back clashes with Glasgow Warriors, on Boxing Day and New Year's Day.
The Warriors began the season as one of the RaboDirect PRO12's form teams but Du Preez believes Edinburgh's recent run puts them in a good position.
"I think they'll be really tough games," he added. It's going to be tough but if we win the battle up front it could decide who wins the game."
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