Gerrard put Liverpool ahead with a cool finish inside the penalty area in the 32nd minute before Aspas, on as a 72nd-minute substitute, tapped home a cross from Suarez, who also played the final 18 minutes, to put the seal on the victory.
Simon Mignolet and Luis Alberto also played the closing stages, while Jordan Ibe and Andre Wisdom were impressive starters for Brendan Rodgers' side.
Steven Gerrard sent the 95,000 crowd home happy with a trademark goal in Liverpool's 2-0 win over Australia's Melbourne Victory at the Melbourne Cricket Ground on Wednesday.
The Liverpool skipper scored in the first half and Spaniard striker Iago Aspas got home in injury time off some Luis Suarez trickery, to seal a hard-fought win over the two-times A-League champions.
Despite an emotional rendition of 'You'll Never Walk Alone" by the capacity red-clad crowd prior to the kick-off, Liverpool struggled to dominate the home side - even though they were missing all their Socceroo stars playing at the East Asian Cup in South Korea.
Every touch made by Gerrard was greeted with a huge roar from the pro-Liverpool capacity crowd, and the Liverpool skipper had a long-range shot beaten away by goalkeeper Nathan Coe midway through the opening half, but Victory were comfortable on the ball, passing it around the pitch for long periods and not overawed.
The Victory produced a much stiffer, more composed performance than the A-League All-Stars thrown together and battered by Manchester United 5-1 in Sydney a few days earlier.
Liverpool got the breakthrough in the 32nd minute when Gerrard interchanged passes with Welsh midfielder Joe Allen before storming into the goal area and firing past Coe.
Gerrard made way on the hour, and then Suarez made his way on to the ground among wholesale substitutions in the 72nd minute.
Suarez is a £40million transfer target of Arsenal and he has made it clear he is keen to move to a team playing Champions League football.
The Uruguayan, playing for Liverpool for the first time for Liverpool since biting Chelsea's Branislav Ivanovic, set up the late second goal as he received a pass from a corner, darted into the area and effortlessly steered a low cross through heavy traffic to allow Aspas to tap home from close range.
It was Liverpool's second win of their Asian pre-season tour after they defeated Indonesia XI 2-0 in Jakarta last weekend. They now head to Bangkok to play Thailand on Sunday.
Full report to follow...