Firefox

Happened to discover this a while ago.

If an ad starts playing in the main window that moves the livestream to a small window in the top right corner, do the following:

1. Mute the main stream.
2. Hover your mouse over to the tiny window and click the PiP button.
3. Unmute the PiP stream

You can now continue to watch the livestream uninterrupted. Once the ad concludes, the PiP pop-up window automatically closes and the main stream continues.

I usually enlarge the PiP window and move it over the ad to cover it.

This is basically a manual method of what add-ons like Alternate Player for Twitch.tv do.