A War That Lasted Under an Hour

The shortest war on record, between Britain and Zanzibar in 1896, lasted well under an hour.
The fighting began on the morning of August 27, 1896, and was over in somewhere between 38 and 45 minutes, depending on which timing you accept. It is widely listed as the shortest war in recorded history.
Check it yourself
Search for the Anglo-Zanzibar War in an encyclopedia. Sources differ by a few minutes, which is itself a nice lesson in history.