Gardner broke the deadlock in the 34th minute, converting a cross from Simon Madden, and then Sean Gregan headed a chance against the bar.
Gregan was one of four senior players included in Dave Geddis' line-up, alongside Stephen Crainey, Seb Carole and Frazer Richardson, but Leeds were facing fresh injury problems today after Richardson left the field with a suspected hamstring strain seven minutes from time.
Geddis said: "It was a good work-out, but in the second half we didn't quite deserve anything more than we got.
"To be fair to Sheffield Wednesday, they really pinned us back and we had to defend strongly."
United's line-up also included youngsters Danny Rose and Jonathan Howson and the game was watched by scouts from a number of Premiership and Football League clubs.