Clarke Odour netted for the Reds in the 69th minute, adding to a strike from Jordan Williams in the 20th minute.
The opening goal came when Williams curled a shot towards the near post which squirmed underneath Cameron Dawson in the Wednesday goal.
The Owls would have been disappointed with the nature of Odour's strike as Cameron Thompson found his teammate unmarked in the area for a comfortable finish.
As with many pre-season friendlies at this time of year, both sides made wholesale changes with the substitutions coming shortly after half time.
Cauley Woodrow captained the Tykes while Jaden Brown made his debut for Wednesday after joining the club earlier this week.