Update two tables, each on separate MySQL servers, on two different machines in one query?

I have two MySQL servers running on two different machines in a local network. I am using PHP and accessing the databases via IP. No problems there. The databases have identical schemas. One of them was an import from the other machine. I want to run a single (ONE) query that updates the same table on each server simultaneously. I already have existing queries and do not want to update them extensively. Is there a simple way to achieve this? I'm looking to keep the databases in sync when an update occurs. I am also open to any other suggestions regarding other ways to keep the databases in sync.