What can be the one word for a person who goes against the odds and finally emerges as a winner.? is "rebel" the correct word?
As stevesliva suggested, you could call that person a dark horse.
A little known, unexpectedly successful entrant, as in You never can tell-some dark horse may come along and win a Senate seat. This metaphoric expression originally alluded to an unknown horse winning a race and was so used in a novel by Benjamin Disraeli ( The Young Duke, 1831). It soon began to be transferred to political candidates, among the first of whom was James K. Polk. He won the 1844 Democratic Presidential nomination on the eighth ballot and went on to win the election. (The American Heritage Dictionary of Idioms)
A competitor thought to have little chance of winning a fight or contest.
'As she had never won in an official competition she was clearly the underdog in the Olympic trials.'
Although there are many words to describe this concept I find that this word is pretty common in the context of competition.