Burton struck in the 47th minute, Tudgay in the 68th, and Laws said that Wednesday dominated the second half.
He made full use of the squad, making many changes at half-time.
"It was a good workout," he said. "We played on Astroturf; we coped with it after a first half in which Haarlem gave us a really good test.
"In the second half we played well; we passed it well, were in control and never looked in danger.
"We used a 4-3-3 system, something that we want to include among our options.
"We also picked up a couple of injuries: Jimmy Smith got a kick on his ankle, but he's okay, and Wade Small dislocated two fingers. They were put back and he should be okay."
Laws was delighted with the fans' backing: "It was a great turn-out and they made lots of noise," he said.
"Our supporters are great. They travel near and far all season in their thousands and even though we have travelled to Holland the fans will still follow, using it as a holiday."
Lee Grant made an early save from Laurens Ten Heuvel, and at the other end Leon Clarke had a penalty appeal turned down.
Two minutes into the second half, the Owls took the lead when Burton, left unmarked, strode forward to open his pre-season goal account after scoring three for Jamaica this summer.
Tudgay coolly tucked his chance away for the second goal.
Wade Small got past the defence and squared to James O'Connor - who had come on as a sub for Smith and the new signing hit a shot low.
It was parried by the keeper to Tudgay, who skilfully turned around his marker to slot the ball home.
Owls: Grant (O'Donnell 75), McMenamin, Hinds, Beevers, Spurr (Gilbert ht), Johnson (Boden ht), Smith (O'Connor 38), Watson (McAllister ht), Esajas (Small ht), Clarke (Tudgay ht), Burton (Lekaj 64).
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The full article contains 418 words and appears in Sheffield Star newspaper.