A double sending off and conceding a late winner conspired to condemn Sevenoaks to a fifth home league defeat of the season.
It was nine versus ten at the end after Baines and Tom Ripley were both dismissed along with Deal defender Charlie Dickens by referee Hossain Tavakolli.
Baines and Dickens both went for challenges Mr Tavakolli worthy of straight reds, while Ripley went for two bookings picked up in the space of as many minutes. Adam Marsh fired Oaks in front after eleven minutes with a good finish inside the right hand post.
He followed up with fierce swerving effort that was saved by young Deal keeper Henry Newcombe and then blasted another effort just wide of the upright. Deal, without an away win this season were given a way back into the game eleven minutes before half-time.
Rene Rivera's run into the box ended when he fell under the challenge of Town skipper John Lord, giving away a penalty earning him a booking - Rivera stepping up to beat Scott Chalmers-Stevens.
Four minutes before half time, Baines became the first red card recipient for his challenge on Charlie Walsh.
Rivera received a yellow card after leaving impressive Aaron McCallum on the turf early in the second half.
Marsh was then denied twice by Newcombe, before Chalmers saved from Rivera. It became ten versus ten soon afterwards when Dickens saw red for another challenge, Oaks then having one effort cleared off the line and sub Kwekil Ansah seeing his effort blocked.
Jack Miles stopped Deal striker Connor Coyne with a timely challenge on the edge of the box, before Deal got the winner three minutes later.
Danny Smith's free kick went across the face of the home goal, finding skipper Dean Hill unmarked who headed home.
Ripley was then booked for a foul on Newcombe at one end, then as play switched quickly to the other - picked up his second for flooring Rivera in the edge of the box.
Chalmers-Stevens pushed another Smith free-kick over the bar, before Luke Bigginton headed over the bar just before the end.