The win was the second Derby victory in three years for Borel, who used a similar stretch run to send Street Sense to the winner's circle in 2007.
Mine That Bird joins Giacomo, who won in 2005, as one of the most unlikely victors in the Run for the Roses.
Mine That Bird covered the 1 1/4 miles in 2:02.66 and paid $103.20 to win.
Pioneer of the Nile held off Musket Man for second, but neither was a match for the unheralded colt from New Mexico.
Friesan Fire, who became the favorite after I Want Revenge was scratched earlier in the day, finished a distant 18th.