Solution:
You simply have to read it with the old pass-phrase and write it again, specifying the new pass-phrase. You can accomplish this with the following commands:
$ openssl rsa -des3 -in server.key -out server.key.new
$ mv server.key.new server.key
The first time you're asked for a PEM pass-phrase, you should enter the old pass-phrase. After that, you'll be asked again to enter a pass-phrase - this time, use the new pass-phrase. If you are asked to verify the pass-phrase, you'll need to enter the new pass-phrase a second time.
