Aspas was again denied by the Valeranga keeper in the 29th minute before Liverpool went ahead moments later. Aspas's lob came back off the bar but fortunately for him, Alberto was there to volley home.
Valerenga hit back almost instantly when Giancarlo Gonzalez got ahead of Jordan Henderson to head in at the near post and ripple Liverpool's net for the first time in pre-season.
Liverpool went in ahead at the break as Aspas put away one of many chances he had in the first half by tapping home Downing's cross.
At half time Brendan Rodgers made 10 substitutions, with Andre Wisdom the only man to remain on the pitch.
Ten minutes after the interval the Reds were two goals clear when Martin Kelly bundled home from close range.
Moments later Kolo Toure smacked the crossbar with a header and the frame of the goal was hit a third time when Fabio Borini curled against the upright 20 minutes later.