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 *)