The game started with a flurry as three goals were scored inside the opening 10 minutes of the contest.
Mohamed Salah broke the deadlock in the fifth minute, turning to convert a corner ball from close range following a Virgil van Dijk flick-on.
It took the Reds just 180 seconds to add to the scoreline, as Salah turned provider, winning the ball in the opposition box to play in Diogo Jota, who slid the ball into the net with the inside of his right boot.
Darmstadt, though, responded to reduce the deficit in quick fashion, with Mathias Honsak racing clear to find the bottom corner of Alisson Becker's goal.
As the game finally settled, both teams exchanged chances, first Christoph Zimmermann shot wide from inside the box, before Dominik Szoboszlai and Cody Gakpo saw efforts saved from distance.
Gakpo again went close a short while later, hitting the side-netting after goalkeeper Marcel Schuhen's clearance fell to the forward out wide near halfway.
Liverpool looked to add a third before the interval, though both Luis Diaz and Alexis Mac Allister saw further chances fall the wrong side of the post.
Alisson was forced into the first meaningful action after the change of ends, as Darmstadt attempted to level proceedings.
Marvin Mehlem and Fabian Schnellhardt both combined in the final third, but were met by the onrushing Reds' No.1, as he got down low to block their advances in the area.
It was Liverpool, though, who opened up their two-goal advantage once again on the hour mark.
Szoboszlai's inswinging corner was met by the run of Diaz, with the winger producing a wonderful flick to find the back of the net and a third of the evening for the Reds.
Diaz was again involved moments later, advancing into the area thanks to some trickery, but substitute Darwin Nunez saw his eventual effort saved.
Ben Doak's introduction from the bench injected Liverpool with more attacking intent on the right-hand side to end the night.
The wide man had a clever run thwarted at the final moment late on after he moved into the six-yard box at pace.
Both Nunez and Joe Gomez saw chances cleared off the line in the final exchanges, with neither team able to add further goals to the scoreline.
Team
Liverpool: Alisson, Alexander-Arnold (Scanlon, 74), Konate (Matip, 60), Van Dijk (Gomez, 60), Robertson (Tsimikas, 60), Mac Allister (Jones, 74), Szoboszlai (Elliott, 60), Gakpo (Quansah, 74), Diaz (McConnell, 74), Salah (Doak, 60), Jota (Nunez, 60).
Unused subs: Adrian, Kelleher, Clark.