You don't need JavaScript for this. Just wanted to make that clear, since as of the time this answer was posted, all of the answers to this question involve the use of JavaScript in some way or another.
You can do this rather easily with pure HTML and CSS by creating a form with hidden fields containing the data you want to submit, then styling the submit button of the form to look like a link.
For example:
.inline {_x000D_
display: inline;_x000D_
}_x000D_
_x000D_
.link-button {_x000D_
background: none;_x000D_
border: none;_x000D_
color: blue;_x000D_
text-decoration: underline;_x000D_
cursor: pointer;_x000D_
font-size: 1em;_x000D_
font-family: serif;_x000D_
}_x000D_
.link-button:focus {_x000D_
outline: none;_x000D_
}_x000D_
.link-button:active {_x000D_
color:red;_x000D_
}
_x000D_
<a href="some_page">This is a regular link</a>_x000D_
_x000D_
<form method="post" action="some_page" class="inline">_x000D_
<input type="hidden" name="extra_submit_param" value="extra_submit_value">_x000D_
<button type="submit" name="submit_param" value="submit_value" class="link-button">_x000D_
This is a link that sends a POST request_x000D_
</button>_x000D_
</form>
_x000D_
The exact CSS you use may vary depending on how regular links on your site are styled.