The hosts were leading 2-1 in Yokohama with 19 minutes remaining when goalkeeper Kawashima let a speculative long-range effort from Gabriel Cichero slip through his grasp and bounce into the net.
That mistake capped an entertaining 20 minutes of second-half action, which saw four goals shared between the two sides in an open encounter.
Aguirre had suffered defeat in his first game in charge - a 2-0 loss to Uruguay on Friday - but looked to be on course for a maiden victory when half-time substitute Yoshinori Muto struck his first international goal with a fine solo effort.
Venezuela - also under new management following the recent appointment of Noel Sanvicente - equalised shortly afterwards through Mario Rondon's penalty, before Gaku Shibasaki's well-taken volley appeared to have given Japan their first win in five.
Aguirre could not have foreseen Kawashima's howler, however, as the hosts were forced to settle for a draw.
Keisuke Honda flashed a shot over in the opening minute as Japan began brightly.
The hosts were almost behind midway through the first half, though, and were indebted to a fine save from Kawashima after a defensive mix-up had let in Rondon.
Another lapse in concentration allowed Luis Seijas to drive forward into space, but the playmaker's strike from distance was wayward.
An incisive move from Japan sent Yoichiro Kakitani clear on goal in the 32nd minute, but the Basel man was denied by the left foot of Venezuela goalkeeper Dani Hernandez.
Hernandez held on to another Kakitani effort a minute later as the game opened up, before Seijas fired wildly off target at the other end.
Seven minutes into the second half, Muto's moment arrived.
The Tokyo man picked up a loose ball on the halfway line and advanced into space before driving a low shot in the bottom right-hand corner from just outside the area.
Japan's advantage lasted just six minutes, as Hiroki Mizumoto brought down Alejandro Guerra and Rondon sent Kawashima the wrong way from the spot.
Shinji Okazaki then teed up Shibasaki for a sweet right-footed volley as Japan edged ahead once more, and they almost doubled their advantage when a 30-yard free-kick from Honda came back off the post two minutes later.
That near miss proved crucial and the visitors secured a deserved draw courtesy of Kawashima fumbling Cichero's shot.
