Wilson struck in the 32nd and 58th minutes to help the Sky Bet Championship strugglers overturn a 1-0 deficit after Leonardo Ulloa had given Brighton the lead.
Yann Kermorgant then curled home a free-kick 15 minutes from time to make it 3-1 to Charlton and, although Ulloa pulled a goal back for Albion in stoppage time, the hosts held on for the points.
The visitors created the first chance of the match after just 68 minutes but Andrew Crofts fired over from 25 yards after Liam Bridcutt had dispossessed Jordan Cousins.
On 10 minutes Charlton skipper Michael Morrison made himself some space on the edge of the box, but his strike was well charged down by Adam El Abd.
Two minutes later returning Brighton forward Ulloa broke down the right, but he failed to pick out Keith Andrews who was well positioned on the penalty spot.
However, it was the Argentinian who put Albion ahead on 22 minutes.
After Will Buckley had cut in from the left and seen a shot blocked, Ulloa picked up the ball and hit it, on the turn, beyond Ben Alnwick from 10 yards.
The Addicks almost responded two minutes later but Cameron Stewart could only shoot narrowly wide, following an important punch clear by Albion goalkeeper Peter Brezovan.
On 24 minutes Crofts shot straight at Alnwick, and full-back Bruno Saltor saw a shot well blocked by Rhoys Wiggins two minutes after.
The visitors seemed in control with Bridcutt beginning to dictate the midfield, and wide man Buckley seeing more of the ball.
But Charlton hauled themselves level just after the half-hour when Kermorgant teed up Wilson, and he curled past Brezovan from a narrow angle.
Five minutes before the interval Bridcutt chested down a Wiggins clearance 25 yards out, and his arrowed strike whizzed inches wide of Alnwick's post.
After 54 minutes Kermorgant burst through on goal and was cynically taken out by El Abd, and the defender was perhaps fortunate to only be yellow carded.
And two minutes later the Frenchman's attempted scissor-kick fell kindly for Wilson inside the box, and the winger rammed home his second of the afternoon.
Brighton tried to hit back and substitute Ashley Barnes nodded a free header over the bar on 67 minutes from Bridcutt's outswinging corner.
And from their next flag-kick Richard Wood was well positioned to nod Matthew Upson's header off the line.
The visitors could not get back on terms though and Charlton extended their lead with a quarter of an hour remaining when, following a foul on Wiggins by El Abd, Kermorgant brilliantly curled the ball into the top corner to make it three.
Brighton refused to give up and Barnes curled against the post with 10 minutes to play, with the follow-up also being struck against the frame of the goal by Inigo Calderon.
Strike partner Ulloa then prodded home in stoppage time for the visitors to make it 3-2, but the Addicks held on to move clear of the relegation zone.