Starting out with a loss against Fabiano Caruana of Italy in the opener, Anand followed it up with a draw in a tense affair against Dmitry Andreikin of Russia, and then desperately needed a win to bounce back in the tournament.
The Indian ace overpowered Morozevich from a typically balanced middle game.
With six rounds still remaining in one of the strongest tournament ever, Anand shares the fifth spot along with Andreikin and world number one Magnus Carlsen of Norway on 1.5 points from three games so far.
Caruana and Nakmura have played all decisive games so far -- losing one and winning two -- while Gelfand and Mamedyarov have one victory and two draws.
The 100000 Euros prize money tournament has thrown many surprises already in the first three rounds and the biggest one is Vladimir Kramnik losing the first two games in the tournament.
Generally solid, Kramnik has struggled with his form here and unless he pulls himself back in a big way, his chances in the event are quite slim.