@Michael Bronson
You will need first to identify the Ambari Service and Component name to be used in the API, this for sure will also bring down the Metrics collector
curl -u admin:admin get http://<AMBARI_SERVER>:8080/api/v1/clusters/<CLUSTER_NAME>/services
Replace the particular service below <Service_name> with the previous output eg AMBARI_METRICS
Stop AMBARI_METRICS
curl -u admin:admin -H 'X-Requested-By: ambari' -X PUT -d '{"RequestInfo": {"context" :"Stop service "}, "Body": {"ServiceInfo": {"state": "INSTALLED"}}}' http://<AMBARI_SERVER_HOSTNAME>:8080/api/v1/clusters/<CLUSTER_NAME>/services/<Service_name>;
The service will stop check the Ambari UI
Hope that helps!!