How to Update Column from column of another table

I have table A and B, A is subset of B. all of A's Primary Key field are in Table B. I need to update some fields in Table A from those fields in Table B.

Structure of Table A
ID
FIELD1
FIELD2

Structure of Table B
ID
FIELD1
FIELD2

Sample Data of Table A

ID FIELD1 FIELD2
1 11 12
2 21 22
3 31 32

Sample Data of Table B

ID FIELD1 FIELD2
1 111 122
2 211 222
3 311 322
4 411 422
5 511 522

How to write the Update command to have the Table A updated to result below?

Table A after Updated

ID FIELD1 FIELD2
1 111 122
2 211 222
3 311 322

There is a way to write SQL update in MSSQL like

UPDATE dbo.Table2
SET dbo.Table2.ColB = dbo.Table2.ColB + dbo.Table1.ColB
FROM dbo.Table2
INNER JOIN dbo.Table1
ON (dbo.Table2.ColA = dbo.Table1.ColA);

Is there any equivalent to do as MSSQL did or I have to write store procedure to this update ?

UPDATE TABLEA SET
FIELD1 = (SELECT TABLEB.FIELD1 FROM TABLEB WHERE TABLEB.ID = TABLEA.ID),
FIELD2= (SELECT TABLEB.FIELD2 FROM TABLEB WHERE TABLEB.ID = TABLEA.ID)

Thank you for your valuable reply. I have 26000 rows in Table B and 2800 rows in Table A. I use a command per your suggestion it takes so long to get it done but it works. Is there any way to make it run faster.

Are there indexes for TableA.ID and TableB.ID?

I got it. Table B has no index. That why it so slow. Actually ID Field of Table A and B is the primary key. But I import the table from other database and I forgot to set the Primary. Now it work so fast. Thank to asking me about the index.