The former Leeds defender committed a horrible error that allowed on-loan Manchester United midfielder Corry Evans to mark his Hull debut with a goal.
But when goalkeeper Brad Guzan brought down Shane Long in the penalty area in the 78th minute, Harte stepped up to claim redemption by slotting home the leveller from 12 yards.
Reading made the majority of the early running and had strong penalty claims waved away when Andy Dawson appeared to bring down Jimmy Kebe in the 18th minute.
Evans replaced Cameron Stewart at half-time and made an immediate impact by giving Hull a scarcely deserved 51st-minute lead. Harte had to shoulder the blame for the goal as he attempted to head Robert Koren's cross back to goalkeeper Adam Federici and succeeded only in leaving Evans with a simple finish.
But Harte was given the opportunity to atone for his earlier error when McAnuff's pass sent Long through on goal and the Republic of Ireland international was brought down by Guzan. This time referee James Linington did not hesitate in pointing to the spot and Harte emphatically slammed home his fifth goal of the season.