Former Rams keeper Grant helped Wednesday secure their third successive draw but the Owls are still perched precariously close to the drop-zone with eight games to play.
Wednesday, without striker Luke Varney, ineligible under the terms of his loan deal from Derby, started in dramatic fashion, Marcus Tudgay slipping the ball to Tommy Miller whose snap-shot from 15 yards cannoned off the legs of keeper Stephen Bywater.
Derby bounced back, former Sheffield United midfielder Michael Tonge's precise corner finding the lanky Chris Porter whose close-range header produced a one-handed reflex save from Grant as he tipped the ball over the bar.
The Pride Park side, playing their part in a fast-flowing game, almost came unstuck as a slick three-man move carved out an opening, Tudgay combining with Leon Clarke before Tom Soares cut inside before his right-foot strike was pushed away by the diving Bywater.
Wednesday were caught napping in the 38th minute when James McEveley found Rob Hulse, who cleverly nipped round the diving Grant but the angle was too tight as he lashed his shot the wrong side of the post.
Grant kept out a Tonge free-kick and served up another spectacular save as Derby took control, finger-tipping Hulse's close-range header over the target after Wednesday had failed to cut out McEveley's free-kick.
James O'Connor was handed a half-chance when he ran onto Clarke's pass but the little midfielder dragged his low shot wide from 12 yards before Tonge powered his free-kick from the edge of the box over the bar.
Substitute Richard Hinds almost found a way through for the Sheffield side stretching to reach Darren Potter's free-kick only for Tonge to clear the ball from under the bar before little midfielder James O'Connor dragged his low shot wide.