It is correct and usable in written English.
You can use it to refer to a situation where someone has more power or authority than someone else. For example, "Although I was upset, I managed to maintain the upper hand and get the outcome I wanted."
A rally-killing double play resulted, allowing the Mets to maintain the upper hand.
Russia is witnessing America's creeping influence with unease and is struggling to maintain the upper hand in its traditional backyard.
It goes without saying that the girls are — marginally — more mature than their male foils and always maintain the upper hand.
In this world, conversations are negotiations in which people try to achieve and maintain the upper hand if they can, and protect themselves from others' attempts to put them down and push them around.
That is not going to change, but so long as we perpetuate the myth that ecology and economy are in competition it is likely that those who are blind to nature's beauty will maintain the upper hand.
Rosberg admitted he was ecstatic to maintain the upper hand over the man who had beaten him to the title in Texas, where a momentary lapse had cost him victory.
The Kassitic nobility, however, maintained the upper hand in the rural areas, their wealthiest representatives holding very large landed estates.
McLaren looks stronger than we thought, and Hamilton maintained the upper hand over Heikki Kovalainen throughout most of the session.
In all life's games, some players are better than others, but randomness maintains the upper hand.
The United States fired one of the first shots in the computer war and has long maintained the upper hand.
Rajoy, a politician who has built his career on riding out storms and waiting for others to make the first move, still maintains the upper hand.
