Play Music in Background in Chrome?

I have a Nexus 4 with rock Android 4.2 and I have a minor annoyance: I listen to Grooveshark and other music streaming acts in the browser, yet I'm unable to listen to hit classics like Taylor Swfit's "Red" when the home button is hit or the screen is turned off. In iOS, I simply could double click the home button and and press play. In Android, however, there's no such option.

Is there a patch or customization I can add to Android to enable audio streaming in the background? I'd prefer to not install apps (limited storage space) just to play music in the background. Alternatively, should I root my Nexus 4 or keep Stock Android? I've been tossing and turning but a stock Android isn't as customizable as Cyanogen Mod was n my Touchpad. Thanks!