Palo Alto, Battle of, May 8, 1846, the first battle of the Mexican War. It was fought near present Brownsville, Texas. Major General Zachary Taylor, with an army of 2,300, occupied disputed territory between the Nueces River and the Rio Grande. He was attacked by General Mariano Arista with about 6,000 men. United States artillery broke up the attack, setting the stage for Taylor's victory the following day in the Battle of Resaca de la Palma.