Chromecast

An appropriately titled lifehacker post: Four Things You Didn't Know You Can Do With Your Chromecast:

"Forget your TV remote—if you have a Chromecast hooked up and always powered on through the usb adapter, you can turn your TV on and even switch to the Chromecast's input with your mobile device."

Sure enough, it worked like magic. I had always been turning on the TV and switching the input.