Hayes and Hooper, who scored 50 goals between them last season in League One, proved a real handful for the visiting defence.
Hooper opened the scoring after 17 minutes when he fired home from the rebound after a shot from winger Martyn Woolford had been only half-stopped by keeper Stephen Bywater.
Derby, who started without a recognised striker, were level three minutes later when the midfielder Paul Green popped up on the edge of the and delivered a good finish with a well-struck equaliser.
Scunthorpe came fighting back with both Hayes and Hooper squandering good chances as they dragged shots just wide of the target.
Hooper was also denied by a good save from Bywater before restoring his side's lead when he broke into the box from the right and found his finishing touch again with an excellent shot low into the bottom far corner for his second goal of the game.
But Green was proving a driving force for the visitors. He almost struck again in the first half and it was he who helped County back on level terms again on the hour when he was brought down in the box by keeper Joe Murphy enabling substitute Kris Commons to make it 2-2 from the spot.
But back came Scunthorpe again and, with just eight minutes remaining Woolford - who got the Wembley winner in the play-off final in May - finished of a flowing move by crashing a right-foot shot low past Bywater.
It was an excellent win for Scunthorpe and just what they needed to bounce back after crashing 4-0 at Cardiff on the opening day of the season.
Hooper opened the scoring after 17 minutes when he fired home from the rebound after a shot from winger Martyn Woolford had been only half-stopped by keeper Stephen Bywater.
Derby, who started without a recognised striker, were level three minutes later when the midfielder Paul Green popped up on the edge of the and delivered a good finish with a well-struck equaliser.
Scunthorpe came fighting back with both Hayes and Hooper squandering good chances as they dragged shots just wide of the target.
Hooper was also denied by a good save from Bywater before restoring his side's lead when he broke into the box from the right and found his finishing touch again with an excellent shot low into the bottom far corner for his second goal of the game.
But Green was proving a driving force for the visitors. He almost struck again in the first half and it was he who helped County back on level terms again on the hour when he was brought down in the box by keeper Joe Murphy enabling substitute Kris Commons to make it 2-2 from the spot.
But back came Scunthorpe again and, with just eight minutes remaining Woolford - who got the Wembley winner in the play-off final in May - finished of a flowing move by crashing a right-foot shot low past Bywater.
It was an excellent win for Scunthorpe and just what they needed to bounce back after crashing 4-0 at Cardiff on the opening day of the season.