The Latics raced into a 3-0 lead inside the opening 42 minutes at the Greenhous Meadow with strikers Danny Philliskirk, who scored twice on his debut, and Adam Rooney, who headed Oldham's third, too hot for Shrews to handle.
Graham Burke, on loan from Aston Villa, pulled one back for the home side just before the interval.
But Oldham continued to look dangerous going forward and lively Dutch winger Sidney Schmeltz hammered home a deserved fourth to seal the visitors' superiority 15 minutes from time.
"It was a fantastic performance from a lot of the lads," enthused Latics boss Johnson. "All of them, to a man, every single one, it was a great performance, and that's what I expect because I know how good we are.
"It's been hurting me the last couple of weeks, certainly last Saturday, how we didn't win that game against Tranmere 4-1 or 4-0 (a 1-0 home defeat)."
Johnson insists his side's firepower in dismantling Shrewsbury did not surprise him.
"I was really pleased and it was coming," he added. "We've played well enough and drawn a couple of blanks, which has been disappointing because we've had some good chances.
"Here things went right and we could have had more goals. I was disappointed not to score more. We probably could have let in another one so there's still stuff to work on, but I'm pleased for all the lads they've had that because all their efforts have deserved a game where we've thumped someone."