"I'm delighted we've pulled that off. It's our first away win of the campaign and it was important to get it," Hodgson said after the match.
"It was a hard-fought and very thrilling cup tie and all credit to Sheffield Wednesday for the way they played and forced us to give of our best.
"We had a good spell of play in the second half but I was wondering if the second goal would actually come because the goalkeeper made a couple of good saves and we hit the post a couple of times but luckily it did come.
"In terms of a cup run, I would be lying if I said it was as important as survival in the Premiership, but it would be nice if we could do both."