You dont need to import it to a staging area. Just run an Execute SQL task as suggested above by dbomrrsm. You will just need to create two sql server connections, one pointing to each of the databases, it doesn't matter if they are not both on the same server, you can chagne which server you want to point to when you create the connection.
You will have to modify the code from dbomrrsm to be safe. Probably something along the lines of:
update databaseA.dbo.tableA
set field2 = databaseB.dbo.tableB.field2....
Im not terribly good at this myself, so if you try this and it doesn't work, hopefully someone else will have spotted the flaw in my suggestion.