The Uruguayan had said in the build-up to Saturday's friendly that he wanted to score in revenge for the 2-2 draw in the league championship in October when his goal put River two up before Boca hit back in the final quarter of an hour.
Mora headed River in front in the 68th minute from Leonel Vangioni's cross and scored again in the 83rd when he broke Boca goalkeeper Agustin Orion's resistance with a fierce right-footed shot.
"River are still the greatest," said their coach Ramon Diaz, while Boca counterpart Carlos Bianchi said: "The superclasico is important to everyone but there aren't three points in play. I was relaxed."
River and Boca, both back under their most successful coaches, will meet twice more in friendlies before next month's start of the "Final" championship, second of two in the league season.
Both sets of fans treat any clash between their teams as life or death affairs, whether in the league or a friendly during the mid-season summer recess as this was in the seaside resort of Mar del Plata, but no incidents were reported.
The build-up to Sunday's Rosario derby between Newell's Old Boys and Rosario Central, on the other hand, has been plagued by hooligan attacks on the rival clubs' premises.
In the latest attack on Saturday, a molotov cocktail was thrown at the entrance to Newell's official shop.
Media reports put the number of police officers who will be on duty at the game at Central's Gigante de Arroyito ground, without away supporters, at between 700 and 900.
Entrepreneur Guillermo Tofoni was quoted in La Nacion as saying: "I'm not organising this clasico again. It would be easier to set up an Argentina-England (match) on the Malvinas (Falkland) Islands."
The Rosario rivals have not met for nearly three years since Central's relegation to the second tier Primera B Nacional in June 2010.