Luis Alberto, Iago Aspas, Martin Kelly and Raheem Sterling all scored for the Reds, who gave up their preseason scoreless streak in the contest but looked very bright on the attack for most of this match.
Liverpool came out humming in this contest, pressing Valerenga from the opening whistle and creating several early chances.
The Reds probably should have gotten on the board in the 15th minute. Stewart Downing won back the ball in the midfield and drove forward before finding Aspas in the clear. But his pass was just a bit short, forcing Aspas to take a dodgy touch before shooting, and Taksdal Kongshavn made the save.
Two minutes later, Aspas left another chance wanting. Jordon Ibe worked down the left flank and found Aspas in the box, but the forward's shot was deflected off a defender.
Ibe nearly scored himself in the 18th minute, cutting back inside and letting it rip. But his near-post effort went wide, a disappointing take for the winger.
Kongshavn came up clutch in the 22nd minute, making two big saves for Valerenga. First, he denied Aspas after a nifty bit of build-up play between the striker and Joe Allen. Then, he recovered to handle Downing's shot from range.
Kongshavn continued to shine, denying Ibe two scoring chances, one in the 23rd minute after a Luis Alberto pass split the defense and sent Ibe in the clear, and again in the 26th minute, blocking Ibe's low shot with his legs.
In the 30th minute, Kongshavn kept his magical night going. This time, he miraculously denied a Downing shot after Jon Flanagan found him with a low cross. The rebound bounced to Aspas but, you guessed it, Kongshavn saved the forward's effort.
But, finally, Liverpool broke through in the 30th minute.
It was a goal Liverpool more than deserved. But it was a lead that wouldn't last very long, as Liverpool would concede their first goal five minutes later against the run of play.
Things seemed to get back to normal after that, with Kongshavn playing the role of hero and Aspas the role of frustrated villain.
But Aspas would get the first half's last laugh.
Liverpool took a 2-1 lead into the half.
It wouldn't take long for Liverpool to add a third.
It wasn't the prettiest tally in the world, but Liverpool wasn't concerned with the style points.
A minute after the goal, Toure almost added his name to the score sheet off a corner, this time connecting with the ball, but his header hit the bar.
Fabio Borini had a close call in the 62nd minute, as he beat both Kongshavn and a Valerenga defender, poking the ball past the pair. But that touch nearly sent the ball out of play, and a scampering Borini sent a shot from a nearly impossible angle spinning across the face of goal and out of play.
Borini would see two more attempts kept out of the nylon. First, Kongshavn got a hand on Borini's shot and steered the ball wide after Raheem Sterling played Borini into a danger area with a nice through ball. Then, a curling effort from just outside the box would hit the crossbar and bounce out of play.
Borini had become the new Aspas—snakebitten.
Coutinho and Oussama Assaidi combined for a clever bit of build-up play before Coutinho flicked the ball toward Sterling, who buried the Reds' final tally.
All in all, a pretty cracking performance from the Reds.
Man of the Match: Stewart Downing, Liverpool
Honestly, you could throw a dart toward five or six pictures of Liverpool players, and whomever you hit would be a fair Man of the Match winner. But Downing was quite good in this game, setting up several attacks and having several of his own attempts rejected by the heroic Kongshavn.
If nothing else, consider this Man of the Match a nice parting gift for Downing.
First of all, how about Kongshavn? He was amazing throughout and stymied Liverpool time and time again, especially in the early going. Liverpool managed three goals, but it easily could have been six or seven.
Beyond that, it was all Liverpool. Alberto and Ibe were wonderful in the first half, while Borini couldn't seem to buy a goal but put himself in excellent positions throughout. Aspas probably should have had more than one goal but was a busy man nonetheless, while Coutinho continued his strong preseason when he was brought on in the second half.
Valerenga may not be on par with Premier League teams, but they're a club in the middle of a season. Liverpool should be quite pleased with this performance, especially from their attacking players.