Bournemouth secured their third straight victory and condemned MK Dons to their fourth defeat in six games.
Lewis Grabban intercepted Jon Otsemobor's weak back-pass to put the visitors ahead.
The Dons' Ryan Lowe was sent off for a reckless lunge on Tommy Elphick after the pair had earlier squared up.
Marc Pugh's rebound made it 2-0 and, after Shaun Williams hit the post for the hosts, Harry Arter's 25-yard drive secured Bournemouth's victory.
VIEW FROM THE DRESSING ROOM
MK Dons manager Karl Robinson told BBC Three Counties Radio:
"I don't condone idiotic behaviour.
"If I think you've done something against this football club you either take it like a man or you walk away and you're gone.
"We all have moments of madness and do silly things, that was completely silly thing and he (Ryan Lowe) be fined internally and he knows that,
"He feels he's let us down and that's all we've got to say on the matter."
Bournemouth manager Eddie Howe told BBC Radio Solent:
"To come here and win 3-0 was really pleasing. I was very impressed with the players and how they responded and adapted to the different challenges in front of them today.
"It's not easy with eleven against ten. We see countless times the ten beat the eleven so we still had a lot to do at half time.
"I thought it was a disgusting challenge [by Lowe] - really really poor. I hope, pray Tommy's not badly hurt.
"We don't know at the moment but it's a knee problem so we'll wait and see. To do that to a fellow professional I think is really poor."