Oldham took the lead after just seven minutes when Jordan Slew turned home James Wesolowski's cross from the right to the bottom corner.
Croft was in the action again moments after the break and he almost restored the two-goal advantage, only for Wednesday keeper Chris Kirkland to parry away.
The visitors got a goal back in the 53rd minute when Jermaine Johnson's low shot from outside the area fizzed past Alex Cizak.
Wednesday went on to level the match soon after when Chris O'Grady nodded home Miguel Angel Llera's delivery.
O'Grady then completed the turnaround with Wednesday's third goal in 17 minutes, beating Cizak with a low finish.
Antonio netted Wednesday's fourth with a drilled shot from the edge of the box with three minutes left on the clock.