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 {
display: inline;
}
.link-button {
background: none;
border: none;
color: blue;
text-decoration: underline;
cursor: pointer;
font-size: 1em;
font-family: serif;
}
.link-button:focus {
outline: none;
}
.link-button:active {
color:red;
}
<a href="some_page">This is a regular link</a>
<form method="post" action="some_page" class="inline">
<input type="hidden" name="extra_submit_param" value="extra_submit_value">
<button type="submit" name="submit_param" value="submit_value" class="link-button">
This is a link that sends a POST request
</button>
</form>
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