How to get browser to ignore password fields on a "change my password" form?

I have a web app (JSP, Spring, Tomcat) and after the user is logged in, they can click a "Change Password" link which prompts them with a simple form with "Password" and "Confirm Password" fields.

<div class="form-group">
    <label class="control-label col-sm-2">New Password:</label>
        <div class="col-sm-10">
            <input type="password" class="form-control" name="password" id="password"  placeholder="Password"  required>    
        </div>
</div>
<div class="form-group">
    <label class="control-label col-sm-2">Confirm New Password:</label>
        <div class="col-sm-10">
            <input type="password" class="form-control" name="confirmPassword" id="confirmPassword"  placeholder="Confirm Password"  required>  
        </div>
</div>

Works fine, except the browser thinks this is a login form and prompts the user if they want to save the password in the browser.

My understanding is autocomplete="false" was intended to prevent the prompting, but modern browsers ignore that field.

Alternately, is there some way to use type="text" and still have the characters displayed as masked bullet characters?