Bradley Johnson had the first real opportunity of the match inside the opening five minutes when he had the chance to head into an empty net, but his finish was just wide of the post.
Alex Tettey thought that he had given the Canaries the lead just after the half-hour mark when he curled the ball in from the edge of the box, but Cameron Jerome was in an offside position in the keeper's line of sight, forcing the officials to chalk the goal off.
Derby immediately tried to put the visitors under pressure down the other end as Craig Bryson attempted to slice the ball in from a tight angle, but a deflection left John Ruddy with a comfortable save.
The visitors responded quickly once the second half got underway, with Jonny Howson teeing up Jerome to smash the ball in from close range.
The Rams were handed a chance to go back ahead just a couple of minutes later when Carlos Cuellar brought down Martin, leaving the striker to score from the penalty spot in his first match against his former club.
Whittaker came close for the away side with just over 10 minutes to go when he found a gap in the Derby defence, but his finish went straight into the side netting.
The Canaries continued to look lively late on, and eventually did find an equaliser when Whittaker pounced on a blocked Nathan Redmond effort in the final minute of normal time, although there was a suggestion of a handball by Martin Olsson in the build up.
Lewis Grabban and Jerome both had efforts in injury time as Norwich passed up chances to steal the win.
The result means that Derby will not return to the top of the table today and remain third, while Norwich sit seventh.