Japan seemed set for their first win under the Mexican but the otherwise reliable Eiji Kawashima fumbled with Gabriel Cichero's 71st minute long-range effort that slipped through his hands much to the dismay of the 64,000 fans at the Nissan Stadium.
The Asian champions twice surrendered lead after substitute Yoshinori Muto had opened the account early in the second half and debutant Gaku Shibasaki, one of the five changes Aguirre made to the side that lost 2-0 to Uruguay on Friday, put them ahead again.
Mario Rondon scored the first goal for the South Americans, converting from the penalty spot after Alejandro Guerra was fouled inside the box.
If the outcome upset Aguirre, who took over after Japan's group stage exit in the World Cup in Brazil led to the resignation of Alberto Zaccheroni, the Mexican did not show it.
"Mistakes are part and parcel of the game and I am just glad that this one came in a friendly," the Kyodo news agency quoted the coach as saying of Kawashima's howler.
"Venezuela were better in the first half. The substitutions went well in the second half and we had to settle for a draw, but we have a four-year project and the new blood in the team made an impact so I am satisfied with that."
Aguirre's team will meet Jamaica in Niigata on Oct. 10 and Brazil in Singapore four days later as they continue their preparations for their Asian Cup title defence in Australia in January.
(Reporting by Amlan Chakraborty; editing by Sudipto Ganguly)
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