At the beginning of the Civil War what would later have been called skirmishes were called battles, so I guess we can call Palmito Ranch at the end of the War a battle.
At the beginning of 1865 the Union and Confederate troops engaged in an informal truce in south Texas, since the War was manifestly about to come to an end, and both sides could see that nothing that was done in Texas would have any impact on the outcome. Negotiations began in March for the surrender of the Confederate troops in Texas but came to nothing. Why a Union force advanced on Brownsville, Texas in May is something of a mystery since a surrender was obviously in the offing. At any rate in a two day fight the Confederates succeeded in causing the Union force of about 500 men to retreat. The Confederate force of 300 sustained casualties of 5-6 wounded and 3 captured. The Union force had 4 killed, 3 wounded and 101 captured. Private John J. Williams of the 34th Indiana had the sad distinction of being the last man to be killed in action in the Civil War. Here is the report of the commander of the luckless Union force: