How to dismiss Heads-up Notifications quickly without clearing them from notification bar?
In stock Android 5.0 Lollipop, it's not possible to dismiss the heads-up notification without clearing them from the notification bar (I had that problem when using fullscreen apps too). AFAIK, this is related to Android framework, and is impossible to be modified by apps (even for Google apps).

However, this is "fixed" in Android 5.1. You can swipe up the heads-up, dismissing the heads-up only, and the notification will still be there on the notification bar.

From Android Police - [Android 5.1 Feature Spotlight] You Can Now Swipe Up To Dismiss Heads Up Notifications Instead Of Getting Rid Of Them Permanently,


  With this feature addition to Android 5.1, you can swipe up to get it out of your way without losing it entirely.