The most reliable sequence I can find to cause an automatic statistics update is:

1. Update statistics sampling zero rows
   This results in an empty statistic object.

    -- Example
    UPDATE STATISTICS 
        Person.[Address] 
        IX_Address_StateProvinceID 
        WITH SAMPLE 0 ROWS;
   

2. Update the target column(s) in a single row of the table
   This increments the column modification counter. The combination of an empty statistics object and an incremented modification counter enables a special case statistics update (it simulates creating statistics on an empty table, then adding a row).

    -- Example
    BEGIN TRANSACTION;
        UPDATE TOP (1) 
            Person.[Address] 
        SET StateProvinceID = StateProvinceID;
    ROLLBACK TRANSACTION;
   

3. Run the query with OPTION (RECOMPILE)
   This causes an automatic update of detected stale statistics, even if a matching plan for the query is already present in cache. The resulting statistics update will subsequently cause an optimality-based recompilation for the original cached plan, if it is matched again.

    -- Example
    SELECT
        A.City,
        A.AddressLine1,
        A.AddressLine2
    FROM Person.[Address] AS A
    WHERE
        1 = 1
        AND A.StateProvinceID = 54
    OPTION (RECOMPILE);
   

###Demo

Using a similar AdventureWorks query as used in jyao's answer, the following script puts everything above together:

DBCC FREEPROCCACHE;
GO
-- Cache a plan for the query
GO
SELECT
    A.City,
    A.AddressLine1,
    A.AddressLine2
FROM Person.[Address] AS A
WHERE
    1 = 1
    AND A.StateProvinceID = 54;
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO
-- Empty stats object
UPDATE STATISTICS 
    Person.[Address] 
    IX_Address_StateProvinceID 
    WITH SAMPLE 0 ROWS;
GO
-- Perform and rollback a single row update
BEGIN TRANSACTION;
    UPDATE TOP (1) 
        Person.[Address] 
    SET StateProvinceID = StateProvinceID;
ROLLBACK TRANSACTION;
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO
-- Run the query again to trigger stats update
GO
SELECT
    A.City,
    A.AddressLine1,
    A.AddressLine2
FROM Person.[Address] AS A
WHERE
    1 = 1
    AND A.StateProvinceID = 54
OPTION (RECOMPILE);
GO
DBCC SHOW_STATISTICS 
(
    'Person.Address', 
    'IX_Address_StateProvinceID'
) WITH STAT_HEADER;
GO

###Output

The DBCC SHOW_STATISTICS results show the original statistics header, the empty header, and the desired updated header at the end of the process: