To my (and my SO's) great shame we've let this happen twice in the last six months due to erratic payment dates and personal schedules (we split some pretty uneven expenses - he does a lot more leisure spending than I do - so we can't really automate the payments... but yes, this boils down to "we were careless.") Both times it just staggered me to think that giving away $6 (or often more!) per MONTH on interest is normal!!
To get back to a rolling zero, though, and avoid the second month pinch Dicey mentioned, just pay them off fully two separate times in a statement cycle (knowledge I'm embarrassed to have acquired the way I did, but let my loss be your gain!)