Obtain something by dishonest or devious ways / trickery. In informal conversation we can use the term wangle which also convey same meaning (to succeed in getting or doing something by persuading someone or by being clever in some way)
He finagled an extra day off from work by telling his boss it was an religious holiday – even though he’s an atheist
He somehow finagled his way into the army as a lieutenant.
If I can think of some excuse to wangle my way out of going tonight I will do!