In Safari's ?General? preferences, change ?Open links from applications? from the default ?in a new window? to ?in the current window.?

Then your new content will open in the current window AND in a new tab.

Interesting, the text is very unclear on this. My reading of this
would be that it would open in the same window and load over
the page I was currently viewing, which would be VERY
annoying. That's awesome, trying now.

This indeed works, awesome. Thanks.

An interesting thing:

Even if you do have the preference item set to open links from applications
in the same window (so they open in a new tab instead of a new window),
Safari still opens in a new window an html document that has been
dragged and dropped onto its icon in the dock. Any workarounds?