The 24-year-old Republic of Ireland international, on loan from Wolves for the rest of the season, conjured up an eye-catching strike as Marcus Tudgay and Francis Jeffers pushed Phil Parkinson's side a step nearer League One.
It was a sweet moment for Jeffers - his first goal of the season after an injury nightmare following his move from Blackburn in August 2007.
Wednesday, without a win in their last six games and cheered on by a massive 30,000 crowd swelled by reduced ticket prices, carved out the early openings with Jermaine Johnson testing Darren Randolph with a long-range strike.
The Sheffield side swept ahead in the 16th minute after on-loan midfielder Michael Gray caused problems with a teasing cross.
The ball was cleared to Potter who lashed in a low right-foot strike from 25 yards, with the ball taking a deflection past the
helpless keeper.
Jeffers had a stinging right-foot shot turned away by Randolph, with the ball falling to Tommy Spurr's whose fierce strike was cut out by the Charlton keeper.
Johnson cut inside and drilled a curling shot which was snapped up by Randolph before Wednesday increased their lead on 38 minutes.
Gray was again the provider with a teasing corner and Tudgay finished with a downward header at the far post for
his eighth of the season.
Jeffers was foiled minutes later as the ex-Blackburn striker took advantage of a Grant Basey mistake to burst through unmarked but his low strike blocked by the keeper's legs.
Matthew Spring hammered a shot from the edge of the area wide of the Wednesday goal before they killed off
struggling Charlton in the 63rd minute.
Gray, signed on a month's emergency loan, found space on the right flank to pump in a low cross.
Jeffers beat Randolph to the ball and turned it over the line from the tightest of angles.
Spring pulled one back four minutes from time with a low strike from 25 yards four minutes from time.
Tudgay had the final word after scoring his second from the penalty spot in injury time after he had been upended by Basey.