Jones had gone into the game on the back of three straight league defeats knowing that another one could push him closer to the sack.
But Jones was handed a lifeline by two-goal Cooper against 10-man Derby who crashed to their first defeat in five games after a run of four successive draws.
Cooper's first came from a 16th minute penalty - only the fourth spot-kick that Wolves have converted from their last 12.
In only his second league start of the season, Cooper then put the result beyond doubt with a 50th minute free-kick.
Derby were always up against it after being reduced to 10 men after goalkeeper Lee Camp was dismissed when conceding the penalty.
Wolves made their breakthrough after Colin Cameron was sent clear by a pass from his fellow Scottish international Kenny Miller.
Cameron raced into the area and was unceremoniously upended by the on-rushing Camp.
Referee Dermot Gallagher had no hesitation in pointing to the spot and dismissing Camp for his challenge.
Derby took off Marco Reich to send on substitute goalkeeper Lee Grant and the first thing that he had to do was pick the ball out of the net from Cooper's well-placed penalty.
Despite the fact they had fallen behind and lost a man as well, Derby could have equalised almost immediately.
It needed a smart save from Michael Oakes to turn away a 20th minute header from Gregorz Rasiak who had met a right-wing cross from Richard Jackson.
That was the only time Derby threatened but Wolves were just as ineffective in attack in the reminder of the first period.
Despite their manpower advantage the only time they created another opening was after 36 minutes when Grant comfortably saved a deflected drive from Miller.
But there was nothing that Grant could do when Cooper put the result beyond doubt four minutes into the second half.
Derby midfielder Adam Bolder was booked for hauling down Miller 25 yards out and from the resulting free-kick Cooper curled his left-foot shot into the top corner of the net.