In poker, the verb "suck out" refers to drawing a good enough card or cards to enable an underdog poker hand to beat a hand that’s the favorite to win.
The noun is commonly spelled "suckout," and means the situation in which the dog hand draws the card or cards to beat the favorite.
An example we read about recently was when Elky, the young French poker champion, was playing in the 2008 PCA Bahamas Main Event. Holding ace-king vs. king-king, he sucked out with an ace on the river, won a pot of more than two million chips, and took the chip lead with only 12 players left in the tournament. He went on to win the tournament; it goes without saying that the timing was more than opportune for such a suckout.
Synonyms are "draw out," "outdraw," and "outrun."
As for whence the expression originates, we looked far and wide, but could find no reference to its etymology. It’s probably another case, common in all jargon, where someone somewhere sometime came out with it, someone else picked up on it and spread it around, and it came into everyday usage.