Yes, leave the phone unplugged until it will no longer turn on. (It helps to do something active with it, like watch video or something.). Then plug in to charge until it is fully charged without unplugging. It's ok if the phone is on while you're doing this, maybe better if it is off. Some people also suggest unplugging when it reaches 100%, wait about 15 seconds, and then plug in again for, say, about 30 minutes to an hour.
It's probably easier to do this on a weekend.
If the phone's battery calibration is off and that is reporting the battery percentage incorrectly, this should fix it. However, it's not always the case that the phone needs to be calibrated - it could be that the battery is failing or you have apps that are draining the battery faster than you'd like.
It's good to know that this helped in this case, though.