Lucas Moura was also excellent and played a role in all three goals.
The Brazilian set up Heung-min Son for the opener before scoring the second himself.
Alli then netted the third goal after an assist from Moura before MK Dons pulled one back late.
Speaking after the game, Son said he felt positive about the club's direction in preseason.
"I have said it before, it is an honour to play for this big club and I just want to continue," he said.
"I have one wish, for the fans to keep supporting us, we will work as hard as possible to make you happy. We have missed them.
"I have only played two games in pre-season but it has been really positive. It is only pre-season but the energy is there, the positivity is there."
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