The “winning card” sense of “trump” spawned a range of figurative uses, including the verb “to trump” meaning “to beat” or “to frustrate by impeding” (“Bob found that his co-worker’s access to Yankees tickets trumped his own diligence in the eyes of his boss”). By the 17th century, “to trump” was being used to mean “to bring forward, to allege” with the sense of concocting an allegation in order to gain an advantage over an adversary. From there it was a short jump to “trump” meaning “to forge, fabricate or invent,” and the “trumped-up charge” was born.
While the evolution of “trump” in this sense sounds straightforward, there is a small loose end I must mention. There was a now-obsolete (last seen in the early 17th century) English verb “to trump” meaning “to deceive or cheat,” derived from the Old French “tromper” of the same meaning. Oddly enough, this word does not seem to have been derived from any form of “triumph,” but may actually be related to “trumpet” in some way.
http://www.word-detective.com/2008/02/trump/