Update table using result of another query

What worked for me (in mysql) was :

update table2, (SELECT RecordID, ROW_NUMBER() OVER (ORDER BY (Value1) DESC) AS Rank 
    FROM Table1) tempTable 
set table2.Rank = tempTable.Rank 
where table2.RecordId = tempTable.RecordId;

Yes, you can have multiple tables in an update in Postgres:

update table2
    set rank = t1.rank
    from (SELECT RecordID, ROW_NUMBER() OVER (ORDER BY (Value1) DESC) AS Rank
          FROM Table1
         ) t1
    where table2.RecordId = t1.RecordId;