According to this post on the official Power BI blog it is now possible to bring your Excel file into a Power BI dataset as a whole (not only importing data); and use portions of it as tiles on your dashboard.
Wow: you can (re)use your carefully crafted charts and amazingly engineered pivot tables in a web-shareable software as a service, not bad.
This is a very interesting feature and adds a range of new possibilities for this recent Business Intelligence Saas.
Now, few considerations.
To accomplish this you need to link an Excel file from OneDrive and the pin-to-the-dashboard option is only available to OneDrive for Business subscribers. So no free beers, sorry.
To pin a chart you actually need to select a range of cells where the chart resides and it will be pinned as an image, much like a print screen, so do not dream of interaction with the rest of the selectors/filters on the dashboard. See what I mean in this picture:
Your chart/table/range will appear in the dashboard as a <div> with a base-64 encoded data:image/png background:
I did not try to embed this tile in a web page, but it could be the next logical step to do.