The Argentina midfielder made a highly anticipated return from a six-month knee injury lay-off and might have sparked a victory at the Bombonera but for good goalkeeping by Nicolas Navarro.
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The defeat leaves Boca in mid-table, 13 points behind Apertura championship leaders Estudiantes, who opened a six-point lead with a 3-0 home win over Lanus on Friday.
Boca and Argentinos, who were coached to the Clausura title at the end of last season by Claudio Borghi who is now in charge at Boca, looked set for a share of the points.
However, a corner in the 87th minute was poorly cleared by the Boca defence and Argentinos defender Santiago Gentiletti swivelled and pounced to shoot the loose ball into the net.
Two minutes later in a counter-attack, Boca goalkeeper Cristian Lucchetti failed to hold substitute Andres Romero's shot and striker Ciro Rius netted the rebound to put the match beyond the home team.
Riquelme, sorely missed by Boca this season, was the best player on the pitch as he engineered what chances the home side had earlier in the match including curling a corner from the left onto the bar.
Striker Martin Palermo brought a diving save from Navarro with a strong header from Riquelme's corner and the playmaker, who had knee surgery in May, had a shot from the edge of the box turned over the bar.
Boca's next match is Argentina's biggest derby, the "superclasico" away to arch-rivals River Plate at the Monumental on November 16. River are away to All Boys on Sunday looking to improve their poor relegation average (taken over three seasons).
Argentinos, improving under coach Pedro Troglio after failing to win in their opening seven matches, are one point behind Boca.
Estudiantes are six points ahead of Arsenal, who drew 2-2 at Racing Club and Velez Sarsfield.
Newell's Old Boys are fourth after a 0-0 draw away to Godoy Cruz in Mendoza.
