Cauley Woodrow struck twice with Alex Mowatt, Jordan Green and Callum Styles also finding the net for the Reds who played some good football, especially in the first half which brought four goals.
Stalybridge’s Neil Kengini fired over the bar when unmarked in the middle of the box in the first minute then Reds goalkeeper Sami Radlinger made a decent save from close range when the ball broke to a home player on the right of the box at a tight angle.
But Barnsley eventually took control of the match and, after Cauley Woodrow hit the inside of the post from 25 yards, they netted twice in three minutes.
Alex Mowatt opened the scoring from the left of the box in the 16th minute as his shot looped over the goalkeeper and in. Jordan Williams was then scythed down on the right of the box and Woodrow netted from the spot.
Radlinger made another decent close-range stop but it was Barnsley who got the next goal in the 39th minute as, after a good move on the left wing, Woodrow received the ball from captain Cameron McGeehan and smashed home with ease.
It was another quick two-goal burst as a move which began with Mamadou Thiam bringing down a superb Mads Andersen crossfield pass ended with Jordan Green bashing a rocket of a shot into the top right corner on the stroke of half-time. Stendel made six changes at half-time then another four after an hour.
Luke Thomas hit the left post from a tight angle on the right of the box then Callum Styles made it 5-0, firing in from low from close range after meeting George Miller’s cross. Miller then looked certain to add a sixth but the goalkeeper brilliantly tipped over his powerful six-yard shot.
First half team; Radlinger; J Williams, Halme, Andersen, B Williams; Green, McGeehan, Mowatt, Thiam; Adeboyejo, Woodrow.
Second half team: Collins; J Williams (Helliwell 60), Moon, Halme (Sibbick 60), B Williams (Moon 80); Thomas, Bird, Styles, Thiam (Marsh 60); Miller, Adeboyejo (Simoes 60), Miller.
Goals: Mowatt 16; Woodrow 19, 39; Green 45, Styles 71.