But John Gregory's side have now gone five games without a win, and time is running out with just 10 matches left.
They were dominant in the first half and looked desperate to turn around their dreadful run of recent form.
Striker Dexter Blackstock, returning from a one-match suspension, appeared to be the main threat and had a great chance after just six minutes.
A piece of trickery from Lee Cook forced former Rangers defender Frank Simek into a slip, and the cross was met by Blackstock only for Iain Turner to pull off a stunning save.
Cook himself was also at his best in the early stages, and he showed his class with an audacious 35-yard pot-shot which caught Turner off his line and hit the bar six minutes later.
The goalkeeper fared better on 15 minutes when he again stopped a looping Blackstock header from Martin Rowlands' cross.
Spanish midfielder Inigo Idiakez was making his Rangers debut following his one-month loan deal switch from Southampton, and he also looked to get in on the act.
A renowned free-kick specialist, the 33-year-old forced Turner into saves from long-range set-pieces on 26 minutes and just before half-time.
But Rangers had gone even closer on 29 minutes, when veteran Paul Furlong shot inches wide after being teed up by Michael Mancienne.
So after barely letting Wednesday get a look-in during the first half, it was a real hammer-blow when the visitors took the lead 11 minutes after the break.
A defensive calamity cost Rangers as a Simek throw was almost ignored by their back-line, leaving Chris Brunt for a simple tap-in at the back post.
It gave the visitors new-found confidence, and Brunt fired over from a similar position again on 63 minutes.
But then Rangers introduced Danish striker Nygaard to inject some life back into their afternoon. On 70 minutes, he saw an effort blocked on the line after he had got on the end of a Cook corner.
And just a minute later, Nygaard went through on goal only to be brought down by Richard Wood for a penalty, which Rowlands converted.
But Rangers have their goalkeeper Lee Camp to thank for this vital point after he pulled off a stunning save from Brunt on 78 minutes.