The Rams had not kept a clean sheet since August and both teams looked frail and nervous at the back whenever the ball was played in the air.
The visitors took a 10th-minute lead through Richard Naylor, only for Derby to score twice in the space of three minutes with Dexter Blackstock and Marcus Tudgay on target.
A trademark free-kick from Jim Magilton brought the game level before half-time, but Blackstock's second restored Derby's advantage shortly after the break.
However, it was a case of two more points dropped for Derby as Matt Richards levelled with just seven minutes remaining on the clock.
This was a match that brought together two teams that made the play-offs last season but are struggling at the other end of the table this term, and it was evident why they are having problems.
Naylor celebrated his new contract with Ipswich by glancing a Magilton free-kick into the top right-hand corner, but Derby soon discovered that the visitors were equally uncertain at the back.
Morten Bisgaard and Michael Johnson wasted good chances before the on-loan Southampton striker Blackstock headed in from close range from an Inigo Idiakez free-kick, which was knocked back across goal by Emerson Thome.
Another accurate cross, this time from Bisgaard, saw Tudgay head powerfully past Lewis Price, but Derby were pegged back three minutes before the break.
Thome fouled Sam Parkin and from 25 yards out, Magilton curled the ball over the wall and into the top right-hand corner. It was a good strike but Kevin Poole left a large part of his goal unprotected and invited the midfielder to try his luck.
The hectic nature of the game continued with Derby punishing another defensive error in the 56th minute.
Fabian Wilnis slipped, allowing Bisgaard to gallop down the right and his cross was swept into the roof of the net from 12 yards by the impressive Blackstock.
The 19-year-old almost completed a hat-trick in the 77th minute when he turned Peter Whittingham's cross onto the top of the bar.
Ipswich always looked capable of salvaging a point and the introduction of Darren Currie proved to be a crucial, as his delivery from Town's left undid Derby's defence.
He had already played in several dangerous crosses and in the 83rd minute he picked out Richards, who placed a glancing header from just inside the penalty area into the bottom left-hand corner.
Derby were rattled and with five minutes left Parkin powered a header towards the roof of the net only for Poole to acrobatically tip the ball over.