If it's a GWT Button just call:
button.click();
see: http://www.gwtproject.org/javadoc/latest/com/google/gwt/user/client/ui/Button.html#click()
but if not and if you don't need do nothing else in java, you can call native method in JS:
private native void click(Element button)/*-{
button.click(); //or jQuery: $(button).click();
}-*/;
If you need use Java code check this: