This can be achieved by doing the following:
curl -D- -u uname:pass -X PUT -d "{\"update\": {\"comment\": [{\"add\": {\"body\": \"Comment added when resolving issue\"}}]}}" -H "Content-Type: application/json" http://localhost:8080/jira/rest/api/2/issue/KEY-12345
I've added a gist here which gives a couple of use cases