The summer signing struck just before half-time, slotting in after Trent Alexander-Arnold’s shot was parried by Anthony Moris.
That goal provided the spark in an otherwise dull first half of few chances at Anfield.
Darwin Nunez missed a big opportunity when he prodded wide from Mohamed Salah’s cross, while Gustaf Nilsson headed over from close range for the visitors.
The excellent Gravenberch was denied a second just after the hour when his dipping effort was pushed behind by Moris.
The Belgian side applied late pressure but Liverpool wrapped up the win when Diogo Jota slotted in after a quick break.
This was not a memorable performance by Liverpool but, after the video assistant referee controversy following Saturday’s Premier League defeat at Tottenham, it was a routine and incident-free win.
Liverpool top Group E with six points from two games.
“Job done,” said manager Jurgen Klopp.
“You cannot only win if you are really exciting. It is good for us as we can learn a lot from this game.
“With rhythm we look one way and without we look another. With exactly the same players. Plenty of things to learn and we will use that.”
Gravenberch catches the eye
Netherlands midfielder Gravenberch, 21, arrived from Bayern Munich but has had to be patient for the opportunity to show what he can do.
His Premier League appearances have been off the bench, with his two previous starts coming in the Europa League and League Cup.
But this was an eye-catching performance by Gravenberch, who produced an all-action display, putting in tackles, creating opportunities and scoring the opener.
He has a goal and two assists in three starts, a return that will likely push him closer to starting in the Premier League.
“It’s great,” Gravenberch told TNT Sports. “It feels super good. It was the best goal of my career so far.
“It doesn’t matter [how it comes]. A goal is a goal.”
This was not a match packed with memorable moments and there was a collective sigh of relief around the ground when Jota struck to avoid any late drama.
But the game will live long in the memory of the Mac Allister family.
Liverpool midfielder Alexis came on at half-time, which meant he faced his brother Kevin, who started the match as a defender for Union SG, for the first time in his career.
While Alexis claimed the bragging rights with Liverpool’s win, it was a good performance by Kevin as he helped frustrate the hosts for long periods.
“Today my dad was here, but I am sure everybody in our family was watching the TV, so it was special,” Alexis said.
“My dad played and knows what it means to play your brother as my uncle was too. I guess he cried a little bit.”
Kevin said: “He [Alexis] is the reason I suffer today but it is a very special moment.
“Liverpool in the last match come to Belgium. It is our revenge maybe, but today I am only thinking in this game with Alexis and my family and now it is the best part of the match.”