Office 365 Exceed Throttling Limit Cause Rest API Error

　

The exception Microsoft.SharePoint.SPQueryThrottledException is thrown since $filter=Title eq 'Female' query causes to walk through the whole list and check every row to see if it matches.

According to MSDN:

The list view threshold does not apply simply to the number of results returned by your query. Instead, it restricts the numbers of database rows that can be accessed in order to complete execution of the query at the row level in the content database.

That's why $top query option is not applicable here.

One option to avoid the issue would be indexing the Title field.

Go to List Settings -> Indexed Columns -> Create a new index -> select Title as a Primary Column:

Once Title field is indexed, the following query should succeed:

https://site/_api/web/lists/GetByTitle('<list title>')/Items?$top=1&$orderby=ID&$select=ID,Title&$filter=Title eq '<value>'