The 36-year-old veteran struck in the 19th minute as Millwall carved open Terry Yorath's struggling Wednesday side to chalk up their second win in a row.
The Sheffield outfit, now with just one win from 11 games, forced the pace in the opening minutes, Leon Knight pulling a low shot wide of the far post and front man Shefki Kuqi heading an Alan Quinn corner over from six yards.
Millwall caught Wednesday napping in the 18th minute when Andy Roberts ran on to a quickly taken free kick but his crisp header flew inches over the top of the bar.
However, Millwall went ahead within seconds when Danny Maddix's poor clearance was snapped up by Neil Harris. He picked out Claridge who twisted to beat Kevin Pressman from 15 yards, the ball going in off the far post.
Wednesday snapped into action - Knight drilled in a stinging shot that was blocked on the line by Tony Warner and midfielder Quinn saw his 20-yard effort stopped on the line by the Millwall keeper.
Claridge was inches away from connecting with a Matt Lawrence cross as the Sheffield side were carved open again in the 31st minute.
Wednesday should have been back on level terms in the 51st minute after Knight's quick feet had Millwall in a tangle. He picked out Simon Donnelly who dithered giving Warner the chance to dive and block his close-range shot.
Warner produced a stunning save minutes later after Trond Soltvedt was upended a yard outside the area. Dutchman Gerald Sibon produced a searing shot which the unsighted Warner managed to punch away.
Claridge almost scored a second goal just before the end as he flashed a shot just wide.
The Millwall marksman then saw his toe-poked shot finger-tipped away by the diving Pressman.