I'm not being cheeky (), so I'll also go with 1890 Wounded Knee as the conventional event of closure.

Except that, of course, if one wants to be very accurate, the last encounter of the "Indian Wars" was won by the Indians. The Indians in question being a group of "Nobbies" (Anishinabe - Minnesota Ojibwe) under Bugonegijig (aka Bugonaygeshi). The location was Sugar Point (Leech Lake), Minnesota. The date was 5 Oct 1898 (in the afternoon), when a US officer and 5 troopers (3rd Inf. Reg.) were killed, and a number wounded - Indian casualties, none.

A settlement was made and full clemency was granted by Pres. McKinley in Jan 1899.

Some refs: Wiki, from the report to the Secretary of the Interior:

The Indians were prompted to their outbreak by the wrongs committed against them and chafed under unfair treatment. They now will go back to their homes and live peaceably if the whites will treat them fairly, which is very likely, as the whites were thoroughly impressed with the stand taken by the Indians. In this respect the outbreak has taught them a lesson.
The Battle of Sugar Point : a re-examination; and The last Indian uprising in the United States.

Ironically, the Ojibwe have worn Army Blue since the Civil War (e.g., K Coy, 1st Michigan Sharpshooters, was mostly Ottawa, but included Ojibwe), in living black & white:



Best for your thesis.

Regards

Mike