Boca's second successive victory in Argentina's Apertura championship confirmed their recovery from a poor start and lifted them to 11th, six points off the pace.
Caruso Lombardi, who had said after Racing's previous defeat to Huracan that he would quit if they lost to Boca, was true to his word by handing in his resignation, local media reported.
Racing, one from bottom without a win, went in front after half an hour when Pablo Caballero turned in a free kick that midfielder Juan Carlos Falcon sent high into the area.
Viatri equalised less than two minutes after halftime when he tapped in the rebound after goalkeeper Jorge De Olivera saved a shot from Juan Roman Riquelme that came back off the post.
The two also combined for the winner on the hour, Viatri netting after Riquelme returned a one-two with his heel.
Boca, who beat Velez on Sunday when Argentina strike Martin Palermo headed a winner from nearly 40 metres, have 11 points from eight matches.
Clausura champions Velez, who beat Argentinos Juniors 1-0, are top with 17 points, but Estudiantes can reclaim the Apertura lead when they play Lanus on Friday.
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