Huracan entered the last-16 clash with just one win from their last seven matches but could take solace from the fact Banfield are also struggling.
Matias Almeyda's men sit 18th in the top flight and had not won since August and that run continued as they were beaten 3-2 on penalties after the two sides were locked at 2-2 through 120 minutes.
And although Fabian Noguera gave Banfield a 33rd-minute lead, Huracan hit back before the break thanks to a Gonzalo Martinez penalty.
Martinez netted again two minutes after the break to delight the home crowd in Buenos Aires but their joy was short-lived.
Emiliano Terzaghi levelled proceedings on the hour-mark and Huracan's chances were harmed further when Ezequiel Gallegos was sent off for a second yellow card two minutes later.
The hosts bravely held on for extra time and eventually, penalties, though, before Huracan goalkeeper Marcos Diaz became the hero.
Diaz saved penalties from Santiago Salcedo and Walter Erviti to start the shoot-out, and although Huracan stuttered, the keeper continued to impress.
And Diaz's excellent one-handed save to keep out Juan Cazares' penalty sealed their progression.
Also in the last 16, Rosario Central beat Tigre 1-0 on Wednesday thanks to Sebastian Abreu's 76th-minute strike.
