His strike four minutes before the break when Ade Akinfenwa flicked on for Tubbs to take a touch and fire past Hatters keeper Mark Tyler.
Akinfenwa might have doubled the score shortly after half-time, but he nodded George Francomb's free-kick against the post from close rage.
Dons boss Neal Ardley said: "The back five including the goalkeeper all communicated well and the midfielders were tireless.
"The front two combined well for the goal and the substitutes did great too at a tough time. It was a complete performance and we could have won by a greater margin."