I use these curl commands to control playback of a kodi media center from a separate computer. For instance, on my laptop I can press Ctrl+Alt+Space to play/pause on the living room HTPC. 

Kodi must have the webserver for control enabled under Settings > Services > Control. The curls need to be adjusted to your specific setup. In these commands I set
http://192.168.0.25:80/jsonrpc
as the destination. Works best if HTPC has a set internal IP, to be set on the router. If a username/password is set on kodi, change to http://user:pass@192.168.x.x:port/jsponrpc