Swindon's first goal of the game came on 14 minutes when Sam Parkin took the ball around the Brighton keeper to score.
Less than one minute later Brighton were once again level when Gary Hart beat Rhys Evans with a 20 yard shot.
In the second half Parkin put Swindon back into the lead with a close range shot after a David Dyke throwing.
Tommy Mooney failed to get on the score sheet, but he did hit the bar with a 25 yard shot which looked to be going over when it dipped to strike the bar.
Mid way through the second half Brighton scored again to make it 2-2, when Brighton who had a penalty turned down earlier in the game were given a penalty.
Henderson took the kick sending Evans to wrong way to make it 2-2.
Overall Swindon were unlucky not to win the game with Swindon having a lot more of the play than Brighton. Swindon's next game is at home to Wrexham on Saturday.