Try adding this between the <form></form> tags
<input type="submit" style="display: none" />
Tested it and it works on Firefox and Chrome. If you have a submit input type in the form, enter should automatically submit it, regardless of whether it’s visible or not.
I am actually using this myself in a login form, though in the username field, it makes more sense to move to the next field than to submit. Just in case you have a similar use case, here’s the code I used (requires jQuery)
$('#username').keypress(function(event) {
if (event.keyCode == 13 || event.which == 13) {
$('#password').focus();
event.preventDefault();
}
});
Note that there is a slight bug though — if the user selects a browser autocomplete username and presses enter, it still moves to the next field instead of selecting it. Didn’t have time to debug this, but if someone can figure out how to fix it, that would be cool.