To obtain, arrange, or achieve by indirect, complicated and/or intensive efforts.
finagle a day off work
To obtain, arrange, or achieve by deceitful methods, by trickery.
finagled his way out of a ticket by pretending to be on the way to a funeral, distraught
To cheat or swindle; to use crafty, deceitful methods. (often with "out of" preceding the object)
...shady stockbrokers who finagle their clients out of fortunes.