Striker Mauro Obolo scored twice in the final five minutes as it was evident that the tiring, 36-year-old Ayala, a libero in a three-man back line, had not played since December.
Ayala, who captained Argentina a record 63 times in his 115 internationals, joined Racing as a free agent last week from Real Zaragoza after 15 seasons in Europe.
He was slow and his timing, normally a key feature of his game, was off. The defence also had little protection from a team without a true holding midfielder that put all their cards on attack with three strikers.
Racing began the Clausura with a promising 3-0 home win over Rosario Central the previous weekend but lost 2-1 away to Colon in mid-week.
Fans, who believed that the signings of two top strikers in Claudio Bieler and Gabriel Hauche plus the arrival of Ayala would make Racing candidates for their first title since 2001, will be revising their aspirations.
Racing took a ninth-minute lead through Matias Cahais but Arsenal, who had not scored in their first two matches, equalised in the 25th when Benfica-bound striker Franco Jara outwitted Ayala.
The home side led again when Hauche scored on the hour but midfielder Diego Galvan equalised with 18 minutes to go before Obolo won it for Arsenal.
Title holders Banfield fielded a reserve side and were beaten 2-1 at Chacarita Juniors. They rested most of their first-team players ahead of their opening South American Libertadores Cup match at home to Mexico's Morelia on Wednesday.
Libertadores Cup holders Estudiantes, who open their defence of the South American title at home to Juan Aurich of Peru in La Plata on Thursday, beat San Lorenzo 2-0.
Velez Sarsfield, winners of last year's Clausura in July, are top with seven points after Saturday's 2-1 home win over Gimnasia-La Plata.
They are at home to Brazil's Cruzeiro, Libertadores Cup runners-up last year, on Wednesday.
