The former Manchester United midfielder capped an excellent display when he whipped the ball past Mark Crossley in the fourth minute of stoppage time.
The defeat was harsh on the visitors and Wednesday probably felt aggrieved because the fourth official had indicated just three minutes of injury time.
Wednesday still deserved to head back up the M1 with at least a point, but Derby have the knack of staging dramatic late finishes.
They beat the South Yorkshire side at Hillsborough with a late goal and Jones' brilliant free-kick was another example of why they have climbed the table since October.
On this evidence there was little to choose between the teams, although Derby carried a bigger threat in attack where Steven Howard surprisingly wasted two first-half headers.
But with Wednesday moving the ball around confidently, play switched from end to end and there was plenty of goalmouth incidents to entertain another big crowd.
Arturo Lupoli had a header blocked by Kenny Lunt and then saw his follow-up shot charged down before Howard headed a cross from debutant Gary Teale wide.
Teale was causing problems down the Wednesday left and Jones was also threatening with his dead-ball deliveries.
But Wednesday had their moments and when Steven MacLean picked out Marcus Tudgay in space on the right, the former Derby man volleyed wide when he could have taken the ball on.
Lupoli scuffed a shot wide just before half-time, but it was Wednesday who almost went in front 16 seconds into the second half when Lunt exchanged passes with Deon Burton before firing in a shot from 20 yards which Stephen Bywater saved to his left.
Derby brought on two more of their midweek signings in Fagan and Stephen Pearson, but Wednesday still played with composure and looked the more likely team to win the game.
The match appeared to be heading for stalemate when Derby launched the ball forward and Fagan got the better of Spur near the right-hand edge of the penalty area.
Spur tripped the midfielder and was booked before Jones beat the defensive wall to give Derby another memorable home victory.