Goals from Fredy Guarin and Rodrigo Palacio put Inter in a commanding position but two goals in four minutes from Alessandro Diamanti and Manolo Gabbiadini pushed the match into extra time.
French referee Fredy Fautrel was left with no choice but to give Hibbert his marching orders but the punishment ended there for Everton as Bajer's curling set-piece rebounded off the woodwork and was cleared to safety.