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With

test = {{15, 11}, {5, 14}, {2, 13}, {3, 5}, {13, 15}, {6, 10}, {8, 15}, {0,2}, {10, 13}, {2, 5}}; 

variations with Ordering in Rojo's answer using Part instead of Extract:

First[test[[All, 1]][[Ordering[test[[All, 2]], 1]]]] 

or

First[#[[1]][[Ordering[#[[2]], 1]]] &[Transpose[test]]] 

or

test[[Ordering[test, 1, #1[[2]] < #2[[2]] &]]][[1, 1]] (* 0 *)