Here's another way, stealing @J.M's test list
test = {{15, 11}, {5, 14}, {2, 13}, {3, 5}, {13, 15}, {6, 10}, {8, 15}, {0, 2}, {10, 13}, {2, 5}}; First@Extract[test, test~Reverse~2~Ordering~1] 0
Remove First to see the whole row
Or probably faster is
Extract[#1, #2~Ordering~1] & @@ Transpose[test]