Paul Sturrock's Championship strugglers looked down and out by half-time and Rommedahl was rested for the second half by Charlton boss Alan Curbishley.
But Wednesday defender Paul Heckingbottom - who has been told he can leave Hillsborough - made a spectacular return with his first two goals of the season to gave Curbishley's men a scare.
Charlton though hung on to claim their first win at Hillsborough for more than half a century.
It was a welcome boost for Addicks boss Curbishley whose side have plunged down the Premiership table with only two wins in nine after their flying start to the season.
The visitors took the lead in the 13th minute when Rommedahl showed his pace down the right, skipped past Chris Brunt and into the area before placing an accurate low shot out of the reach of keeper David Lucas.
Three minutes later Wednesday produced a spirited reply and were back level. Chris Brunt's deep corner was headed back across the face of goal by skipper Graham Coughlan and Heckingbottom leapt above the rest to head in the equaliser.
Wednesday were almost gifted an own goal after 23 minutes when Brunt - a constant threat from the left - curled in a testing cross and Bulgarian Radostin Kishishev almost glanced a header past his own keeper.
Three minutes after that stand-in skipper Matt Holland punished the home side when they dithered. Bryan Hughes fed the former Ipswich Town star who carried on his surging run and crashed his shot past Lucas.
Again Wednesday had their eyes on a swift reply and broke quickly but new boy Marcus Tudgay - who scored on his debut on Monday - cracked a low effort just wide and failed with an ambitious overhead kick.
A minute before half-time the game was already beyond Wednesday when Rommedahl claimed his second goal.
And it couldn't have been easier as the timid home defence backed off to allow Darren Bent to slip the ball out wide to Rommedahl who was allowed time and space to place his shot into the open net.
Burton O'Brien was wide with another long-range effort before Heckingbottom pounced again with a close-range finish after Charlton failed to clear an awkward ball.
And Bent had the last word as he raced onto a long ball from Darren Ambrose, coolly rounded Lucas and slotted the ball into an open net.
Sheffield Wednesday - Paul Heckingbottom. Scored a rare brace even though his days at Hillsborough appear to be numbered.
Charlton - Matt Holland. Back to his best after enduring a difficult season at The Valley, his goal that restored his side's lead proved to be crucial.