The Golden Eagles (23-7) will face fourth-seeded Rutgers in the quarterfinals Sunday.
Trailing 44-37 midway through the second half, Marquette rallied despite leading scorer Angel Robinson sitting on the bench with four fouls.
Jasmine Collins hit back-to-back layups to make it a three-point game.
Marquette was down 53-49 after Taneisha Harrison’s 3-pointer with 8:02 left. The Golden Eagles scored the next nine points to take a 58-53 advantage on McMorris’ pullup in the lane with 4:16 left.
Pitt was able to get within two twice, but Collins’ layup with 15.7 seconds left sealed the win.
Harrison scored 27 points while Shayla Scott had 11 points and 13 rebounds to lead Pitt (14-17).