The Ireland international salvaged a share of the spoils for Gary Bowyer's team in their season opener following Johnny Russell's opener before half time
Best hooked a loose ball home from inside the penalty area after the hosts failed to clear a Chris Taylor cross from the right in the final minute of normal time.
Derby's new signing Johnny Russell thought he had given his new side the victory with a goal just before the break after Alex Marrow had handled in his own penalty area.
But both teams had to be content with a point in the end, as they got their respective Championship campaigns under way in entertaining fashion.
Russell's fellow new Pride Park arrival Lee Grant was named in the starting line-up and the experienced goalkeeper was crucial in keeping his side in the game in the opening 20 minutes.
He saved well at the feet of dangerman Jordan Rhodes in the opening minutes and patrolled his area well.
The visitors had looked the stronger but the forced substitution of Ruben Rochina knocked them back, and soon after Derby opened the scoring as Russell sent Jake Kean the wrong way with his emphatic spot kick..
Best, who had replaced Rochina, had a fantastic chance to equalise early in the second half but he was unable to convert a low cross from Alan Judge from two yards.
The striker saw another good opportunity wasted as Gary Bowyer's side pushed for an equaliser, but their pressure paid off as he converted his third chance with an instinctive finish.