Champions Velez Sarsfield also turned on the style to beat Banfield 3-0 at home as they went joint top with Boca with four points apiece after two matches of the Apertura championship.
Boca fans lit candles wrapped in the badge of River Plate, who were relegated in June, and chanted "we won't be playing with the chickens ever again" before the start of a match played in almost constant drizzle.
Viatri, making the centre-forward role his own after the retirement at the end of last season of Boca idol Martin Palermo, put the home side ahead after 45 seconds when he scored from Walter Erviti's cheeky backheel.
Boca scored three more goals in the final 10 minutes with Viatri slotting home his second in the 80th from substitute Nicolas Colazo's low left cross.
Playmaker Juan Roman Riquelme, who had a part in the first two goals, tucked a fine third inside the far post in the 84th and Colazo completed a night of misery for Union goalkeeper Enrique Bologna and his defence in the 86th.
Velez, held 1-1 at Godoy Cruz in their opening match, went ahead with a penalty by Santiago Silva in the 21st minute after left back Emiliano Papa was brought down.
Five minutes after the interval, playmaker David Ramirez won a corner when his shot from the right was well saved by Cristian Lucchetti. Ramirez took the corner and found centre-back Fernando Ortiz, who headed the second.
With seven minutes left and after Silva had hit the post, his fellow striker Juan Manuel Martinez scored the third with a shot that went in off the underside of the crossbar.
San Lorenzo bounced back from a 1-0 home defeat by Lanus to upset Estudiantes 2-0 in La Plata scoring two goals in less than two minutes just past the hour.
Busy midfielder Gabriel Mendez scooped the ball forward as he fell in a tackle near the halfway line and striker Emanuel Giglioti, a new signing from All Boys, shot low under Paraguay goalkeeper Justo Villar to open the scoring on the hour.
A minute and a half later, Mendez ran onto a left cross into the box, rounded Villar and clipped the ball into the empty net.
River make their Nacional B division bow against Chacarita Juniors at the Monumental on Tuesday.
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