After a goalless first half, Liverpool - who also had Danny Ings in the side - fell behind to Reiss Nelson's fifth PL2 goal of the season.
Rhian Brewster equalised after 70 minutes with an excellent left-footed strike.
Hart, a 20-year-old defender, pictured above left, struck at the death to send Liverpool three points clear of Arsenal at the top of Division 1.
Arsenal travel to Manchester United on Friday 8 September and Liverpool host Manchester City two days later.
See: PL2 Division 1 table