The Sheffield side stormed back with a strong second-half performance with Songo'o, on loan from Portsmouth, playing a starring role.
Wednesday, undefeated in eight games, had started strongly and were handed a half-chance when Deon Burton was given too much space in the area and his chipped shot from 12 yards dropped the wrong side of the bar.
Cresswell tried his luck with a low strike smothered by the diving Lee Grant, before the ex-Wednesday striker almost found a way through after exchanging passes with midfielder Liam Lawrence, but Grant dived to save at his feet.
The pace hotted up as Wednesday had a penalty claim turned down when Songo'o's cross from the right found Sean McAllister and then smacked against centre-back Chris Riggott's arm.
The Sheffield side went even closer minutes later with midfielder Songo'o this time picking out defender Richard Wood, whose fierce strike took a deflection as Carlo Nash tipped the ball against the bar.
Tempers flared as loan signing Shola Ameobi was booked before Stoke snatched the lead in the 21st minute.
Lawrence was the architect with a quickly taken free-kick, Wood cleared the ball to the lurking Stephen Pearson, whose hopeful angled drive from 20 yards was cleverly flicked in from close range.
Stoke looked for a second goal and it almost came five minutes before the break with the Lawrence-Cresswell partnership working again as the former drilled in an angled shot which was pushed around the post by Grant.
Cresswell blundered minutes after the restart as the Wednesday back four were caught flat footed as they failed to cut out Rory Delap's long throw from the right.
However, the Stoke goalscorer mis-timed his header as Grant saved comfortably.
Israel international Ben Sahar was given too much space in the 61st minute, but the teenage striker on loan from Chelsea fired inches wide from 20 yards after clever work from Burton.
But the Owls refused to throw in the towel and Songo'o's superb late strike secured a vital point in their battle to avoid relegation.