Mohamed Salah, Sadio Mane and Roberto Firmino were named on the bench as the likes of Diogo Jota, Divock Origi, Xherdan Shaqiri and Takumi Minamino were handed starts in the attack.
The Danish side should have been ahead in the third minute after Alexander Scholz sent Anders Dreyer clear on goal but goalkeeper Alisson rushed off his line to make a crucial save.
The hosts were struggling to build momentum, with Midtjylland pressing them high and they were dealt an injury blow on the half-hour mark after Fabinho went down with a hamstring problem and was replaced by 19-year old defender Rhys Williams.
However, Klopp's charges were growing in the game towards the end of the first stanza and the closest they came to breaking the deadlock was on the stroke of half-time through Minamino's glancing header that missed just wide from Trent Alexander-Arnold's cross.
Diogo Jota finally broke the deadlock ten minutes inside the second stanza with a tap-in in the centre of the six-yard box from AlexanderArnold's cut-back.
The Reds kept the visitors on the back foot with the introduction of Mane and Salah, who both came on for Minamino and Origi but they lacked the final pass in the last third.
However, the hosts were were nearly punished after Evander carved out space inside the box and unleashed a low strike on a turn that sailed slightly wide of the bottom corner.
Firmino had a wonderful chance to put the game to bed for Liverpool in the last two minutes after receiving a cut-back from Alexander-Arnold but he blasted his shot over the bar while Dreyer squandered a one-on-one chance with Alisson at the other end.
Salah eventually wrapped up the game for the Reds in stoppage time with an unstoppable spot-kick after he was brought down inside the box by Paulinho.