Tom Clarke went close to giving Orient an 11th-minute lead in Saturday's League One clash at Hillsborough when he headed against the bar after meeting Leon McSweeney's cross.
But the only goal of the game came in the 19th minute when Ben Marshall touched a free-kick to Chris Lines, whose cross was headed in by Johnson at the far post.
Ryan Lowe threatened to add a second soon after when he was free inside the area but keeper Ben Alnwick got down smartly to block.
The impressive Marshall had an effort deflected over and a strike from Johnson was disallowed after the referee spotted an infringement. Lines put a free-kick on target which was easily saved, while Orient's David Mooney volleyed wide in the closing stages of the first half.
Wednesday continued to press in the second half, with Johnson's angled shot hitting the side netting and Miguel Llera heading off target. Orient skipper Matthew Spring came to his side's rescue when he cleared Chris O'Grady's header off the line.