The trick is to turn your weight opposite direction of your fall (usually toward the moving leg) and by weight i mean your arms. For example, if you're falling slightly on your left, put your weight to your right by contracting left pecs and/or extending your right pecs. If it's still not enough, you need to rotate your chest (which is very dangerous because chest is very strong, it can totally wreck you balance if not carefully managed). That's some basic info, I want you to think what to do not just listen to some internet person.
Btw, you should hold or contract your neck, don't let your head dangle. Also running with a relaxed chest is kinda dangerous imo