The Battle of Palmitos Ranch, the last land battle of the war--and a Confederate victory--was fought more than a month later, on May 12-13. The war at sea continued, as the CSS Shenandoah captured a Yankee whaling fleet in the Bering Sea, probably saving hundreds of whales. One might say the war was finally over when the Shenandoah docked at a port in England and struck its flag on November 22, 1865.
Or when Raphael Semmes surrendered the CSS Alabama in England. Well after Appomattox and Bennett Station surrenders.