Definition from Wiktionary, the free dictionary
- (transitive) To obtain, arrange, or achieve by indirect and usually deceitful methods.
- ...finagle a day off from work.
- 2012 May 24, Nathan Rabin, “Film: Reviews: Men In Black 3”, The Onion AV Club:
- Sequels to fish-out-of-water comedies make progressively less sense the longer a series continues. By the time Crocodile Dundee In Los Angeles rolled around in 2001, 15 years after the first Crocodile Dundee became a surprise blockbuster, the title character had been given an awfully long time to grow acclimated to those kooky Americans. Men In Black 3 finagles its way out of this predicament by literally resetting the clock with a time-travel premise that makes Will Smith both a contemporary intergalactic cop in the late 1960s and a stranger to Josh Brolin, who plays the younger version of Smith’s stone-faced future partner, Tommy Lee Jones.
- (transitive, intransitive) 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.
Derived terms 
(transitive) to obtain or achieve by indirect and usually deceitful methods
(ambitransitive) to cheat or swindle; to use crafty, deceitful methods (often with "out of")
- finagle, The Word Detective, February 12th, 2008