The on-loan Real Valladolid forward showed why he was recommended to the Rams by Spain coach Vicente del Bosque as Nigel Clough's side won for the first time since the opening day of the Championship season.
Bueno opened the scoring in the first half and when on-loan Palace striker James Vaughan, who spent a spell on loan with Derby last season, was sent off after just 20 minutes for a tackle on John Brayford Palace capitulated.
Kris Commons added a second before half-time and further strikes from Bueno, Paul Green and Shefki Kuqi condemned sorry Palace to their fourth away defeat without scoring this season.
Derby made a bright start and took the lead with a fine move 13 minutes in.
Brayford was sent clear by Green down the right and the full-back looked up and picked out the onrushing Bueno, who swept the ball home with a neat right-foot finish.
The Rams were causing Palace all sorts of problems with their passing and movement and the visitors' hopes of getting back into the game were dealt a major blow when Vaughan was dismissed after just 20 minutes.
The on-loan striker caught Brayford with a late challenge and referee Tony Bates wasted no time in pulling out the red card.
Kuqi was unfortunate 10 minutes before half-time when his shot from the angle came back to him off the post. The burly striker then showed great awareness to pick out Green but the unmarked midfielder somehow fired wide of the empty net.
But Derby doubled their lead five minutes before the break with another fine move when Commons exchanged passes with the impressive Brayford and beat Speroni with a measured left-foot finish from the right side of the penalty area.
Palace showed some fight early in the second half but they were three goals behind after 61 minutes when Brayford and Green combined to great effect once again.
Green was sent away down the right by Brayford and the Republic of Ireland international's cross was deflected into the path of Bueno, who beat Speroni with a fine right-foot finish.
Green was rewarded for a fine display with a goal of his own six minutes later, when he nodded home Robbie Savage's inviting free-kick.
Palace were in disarray at the back and former Derby defender Claude Davis gifted them a fifth goal when Kuqi nipped in to beat Speroni to the defender's poor backpass and tucked the ball home.
And only a fine save from the overworked Speroni denied Bueno, who was brimming with confidence, a hat-trick seven minutes from time.