With the original tie postponed due to a waterlogged pitch, there was much talk of a potential Steel City quarter-final tie if Wednesday won through, with the draw pitting the winners against League One outfit Sheffield United.
However, goals from Callum Harriott and Simon Church either side of Leon Best's equaliser ensured it will be Powell's men who visit Bramall Lane to battle it out for a place in the semi-finals.
Despite a 1-0 win over high-flying QPR on Saturday, Charlton remain in the bottom three of the Championship, and Powell said the cup was providing a welcome distraction.
"We are party-poopers in Yorkshire," he told BBC Sport.
"We needed to score when we were on top and we did but they worked us hard after the break.
"Our keeper Ben Hamer made some cracking saves but that's cup football.
"It's not been the greatest campaign - that's an understatement - but this means a lot.
"That's two huge results in 72 hours. You savour these moments because there have been plenty of dark moments."
Opposite number Stuart Gray was left frustrated as Wednesday missed out on a golden opportunity to reach the last eight for the first time since 1997.
"It wasn't acceptable," he said.
"The first half is the worst since I've been here - maybe it was the occasion, I don't know.
"We've let the fans down. This was a great opportunity for us. If we play like we have been (doing), we win. It just wasn't us."
