Toranzo bagged his brace in the second half as the Argentinian visitors edged closer to qualifying for the group stages at the Estadio Alejandro Villanueva in Lima, Peru.
Huracan - participants in the Copa Libertadores as winners of the 2013-14 Copa Argentina - made a dream start to proceedings against Alianza, when Ramon Abila broke the deadlock in the fifth minute after being played through with a no-look pass from Toranzo.
It got better for Huracan seven minutes before half-time, Alejandro Romero pouncing on an embarrassing defensive blunder just outside the six-yard box to double the lead.
Two goals from Toranzo inside the final 14 minutes virtually guaranteed Huracan a spot in the group stages ahead of next week's return leg in Buenos Aires.
Huracan and Alianza are playing for a spot in Group Three, which consists of Cruzeiro, Mineros and Universitario.
At the Estadio Morelos in Mexico, hosts Morelia played out a 1-1 draw with Bolivian outfit The Strongest.
Pablo Escobar gave The Strongest a ninth-minute lead through a free-kick that snuck in at the front post.
Morelia were back on level terms nine minutes before the break after David Depetris headed home from close range.
The Strongest will be back at home in La Paz next week, hoping to join Emelec, Internacional and Universidad de Chile in Group Four.
