An entertaining contest saw both teams spurn leads before Al Gharafa's Brazilian striker grabbed the decisive goal 12 minutes from the end.
Al Khrityat opened the scoring through Ahmed Kahil but they fell behind to a second-half double from Farhad Majidi. Majidi scored from the penalty spot on 56 minutes and added another on 71 minutes.
Al Khrityat levelled scores again five minute later, with Yahia Kiepi on target, but moments later Tardelli scored his winner to move the visitors six points clear of second-bottom Al Khrityat.
Al Ahly remained at the foot of the table as they were beaten 1-0 at Qatar SC, with Fadel Omar hitting the winner on 26 minutes.