The Owls had the better of the chances against Nigel Clough's side but a combination of some wasteful finishing and some resolute Derby defending denied the home side a precious three points in their battle to avoid the drop.
Alan Irvine's side have now won only one of their last eight games and are in real danger with eight matches remaining.
Derby also look destined for a nervous end to the season, with Clough's men only four points better off than the Owls.
Wednesday should have taken the lead in the first minute when Shaun Barker's attempted clearance was charged down and fell kindly for Tommy Miller, but Stephen Bywater was alert to the danger and made a fine save to deny the former Ipswich midfielder.
Miller was almost made to rue that miss less than a minute later when former Sheffield United midfielder Michael Tonge swung in a corner from the left and Chris Porter rose highest to power a close-range header which was tipped over the bar by Lee Grant.
Wednesday came close once again after 14 minutes but Marcus Tudgay failed to bundle home Miller's inviting cross under pressure from two Derby defenders.
Both sides looked dangerous going forward in the first half and Rams left-back Jay McEveley whipped in a dangerous cross which appeared to be diverted wide for a corner with Porter poised to pounce, although referee James Linington signalled for a goal-kick.
Tom Soares looked threatening cutting in from the left for the home side and the on-loan midfielder stung Bywater's palms with a rasping right-foot drive 26 minutes in.
Hulse, another former Sheffield United man, then had three chances to silence the Wednesday crowd before the break.
The big striker fired wide at the near post after showing some quick feet and then had a towering header tipped over by the agile Grant before heading a Tonge corner wide from close range, although referee Linington mysteriously awarded a corner.
The second half failed to live up to the opening 45 minutes with both sides showing why they find themselves embroiled in a relegation battle.
But Derby were indebted to Tonge when the midfielder back-pedalled and headed off the line after a looping header from Lee Beevers looked destined to find the back of the net.
And the outstanding Barker came to the Rams' rescue with 16 minutes remaining when Soares capitalised on some indecision between Bywater and Russell Anderson and pulled the ball back towards the empty net but Barker was alive to the danger and nipped in front of Francis Jeffers to turn the ball behind for a corner.
Wednesday threw everything at Derby in the closing stages but Barker and Anderson stood firm to frustrate the Owls.