You can actually do an "online" upgrade via SSH if you want to using host profiles.
1. Enable HTTP Client Firewall Exception
esxcli network firewall ruleset set -e true -r httpClient
2. List Profiles
esxcli software sources profile list -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml
3. Choose and install profile
esxcli software profile install -d https://hostupdate.vmware.com/software/VUM/PRODUCTION/main/vmw-depot-index.xml -p ESXi-5.1.0-799733-standard
- Might need option --ok-to-remove