Manager Jos Luhukay admitted Sheffield Wednesday made hard work of booking a Carabao Cup second-round clash with Premier League Wolves.
The Championship Owls beat League One Sunderland 2-0 at the Stadium of Light to set up a Hillsborough tie against top-flight opposition but didn't have things all their own way.
They took a first-half lead against the run of play through Marco Matias' opportunist strike before improving after the break and sealing their victory through Adam Reach's glancing header.
"It was not an easy game," Luhukay said. "Sunderland played very well. In the first half they had good chances to score the first goal. We had some chances but our finishing didn't lead to a goal."
Wednesday switched at the interval from three at the back and went with more of a 4-1-4-1 shape to combat the Black Cats' threat.
"We had in the first half problems in closing down the running player from the midfield," Luhukay added. "We didn't find it easy to stop them.
"In the second half we changed our formation and then I think we had more control in the midfield and the defending. There were not a lot of a spaces then. That was positive for us."
It was the Owls' first win of the season after an opening-day 3-2 defeat at Wigan Athletic and a 1-1 home draw with Hull City last Saturday.
Next up is a trip to Brentford on Sunday.