In a superior position; at an advantage: I always try to be one-up(1919+)
Ahead by one: The Pinks were one-up on the Puces, 109 to 108
To get the advantage over: I wasn't trying to one-up Arthur Schwartz
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with one-up
Having an advantage or lead over someone, as in Sara is one up on Jane because she passed algebra in summer school. This expression comes from sports, where it means to be one point ahead of one's opponents. It was transferred to more general use about 1920.