Its not the battery, youre experiencing a classic wakelock, some app is prevention the phone from entering deep sleep/hybernation.
Solution is to either remove the culprit app, or reign it in. Check the battery usage stats what has been draining power. Or Use betterbatterystat to find what is causing the wakelock. Usually Google Play store is the culprit, which we need installed.
Greenify will help your phone hibernate apps when the screen goes out. Thi k this might rewuire root though.
Localisation settings could also be keeping the phone woken.