Chris Eagles curled home from 25 yards, then converted from the penalty spot after Nathan Doyle's handball and looked on from the bench as Chris Iwelumo wrapped up Tuesday night's win - all three goals coming during a one-sided second period.
Laws, whose side drew 3-3 at Sheffield United last weekend having conceded four minutes into injury time, admitted it was important his side bounced back after their deflating trip to Bramall Lane.
He said: "I thought it was a great performance. Especially on the back of the Saturday when we felt we'd lost the game.
"The players were depressed after losing two vital points and it was important that on the back of that we came up with a performance, and the pressure was on us to get the win.
"It was never going to be easy. Barnsley are a good side and it showed during the first 20 minutes. They edged it and caused a few problems.
"My man of the match was Leon Cort. He made two critical tackles when it was 0-0. That kept us in the game and the first goal was always going to be key.
"The performance in the second half was sublime."
Eagles, who has starred for the Clarets this season with a string of glittering displays, scored his fifth and sixth goals of the season and Laws was quick to hail the success that the 24-year-old former Manchester United winger is currently enjoying.
"He's unplayable when he's in that confident mood," he added. "He's in great form, especially when he's prepared to do all the running and chasing.
"He did too much of that and ended up getting cramp so we took him off and saved him for Saturday.
"Obviously Chris will get the plaudits because he's in sensational form and he's a top player. When he plays like that he's incredible and is exciting to watch."
Barnsley boss Mark Robins was left scratching his head after yet another away defeat.
The Tykes, who managed a 3-1 home win over Nottingham Forest last weekend, were never at the races and are one of only three sides - along with Tuesday night's opponents and Middlesbrough - without an away win this season.
"We did alright for 45 minutes," he said. "But as I've just told the players, for away games I may as well just come in here and read a statement.
"As soon as we concede a goal we capitulate. We've got to be better than that and we are better than that, but we're just not showing that.
"I must have put together a team that only like to play at home and don't like travelling."