The Canaries, buoyed by their 5-1 derby demolition of Ipswich on Thursday night, broke the deadlock on the stroke of half-time when in-form striker Jackson headed home Marc Tierney's cross from close range - his sixth goal in as many games.
But Derby levelled nine minutes into the second half when the unmarked Steve Davies headed home an Alberto Bueno cross.
The home side, though, moved back in front six minutes later when Jackson spotted Rams goalkeeper Brad Jones off his line and superbly chipped the ball in.
Nevertheless, the resilient Rams levelled once more three minutes later when Bueno lashed a shot into the bottom corner from 20 yards.
However, with Norwich seemingly having to settle for a draw, Jackson bundled home to raise the roof at Carrow Road.
It keeps City second, a point ahead of Cardiff who won 1-0 over Preston at Deepdale, with two games to go and delayed QPR's promotion to the top flight.
There was an early delay when Derby defenders Shaun Barker and Daniel Ayala clashed heads before the first chance fell to the on-fire Jackson but the Canada international volleyed wide from 12 yards.
The Rams had a sight of goal themselves in the 10th minute but Theo Robinson's 25-yard drive was comfortable for City goalkeeper John Ruddy.
Norwich came close to taking the lead in the 15th minute. Andrew Crofts' header from a Tierney cross was well saved by Jones, with Grant Holt just unable to bundle home the rebound.
Jones was called into action again three minutes later, palming a shot from Jackson over the bar.
Derby were looking to hit Norwich on the break and Gareth Roberts shot wide in the 25 minute and Stephen Pearson did likewise moments later.
In between, City midfielder David Fox struck a speculative volley down the throat of Jones while Holt headed another over as half-time approached.
But the Canaries moved in front just before the break with Jackson's bullet header.
However, the visitors silenced Carrow Road in the 54th minute when Davies nodded in a cross from Bueno, who moments later fired a 20-yard free-kick just wide.
The home fans, though, were back in full voice on the hour when Jackson, brimming with confidence, exquisitely chipped Jones.
Minutes later the nerves were back as Bueno levelled with a fine strike from just outside the box.
Norwich came close to going ahead for the third time but a stunning point-blank save from Jones kept out substitute Rob Edwards' header from an Andrew Surman corner.
Another sub, Henri Lansbury, then let fly from 30 yards which a fully-stretched Jones tipped over.
The Canaries were piling forward in a desperate search for the winner but Derby came close to taking the lead but Ruddy was equal to John Brayford's 20-yard strike.
Then in the final minute of injury time, Norwich won it through Jackson, his second treble in three home games.