Virgil van Dijk's header inside the opening quarter-hour was matched by Mohamed Salah's injury-time breakaway finish in the closing moments to ensure the Reds further bolstered their lead at the summit.
However, Jurgen Klopp's side could have doubled their advantage inside the opening half-hour on Sunday were it not for the intervention of the video assistant referee.
The Brazil international looked to have scored his first goal at home this season after Sadio Mane fed back a failed United clearance to him on the edge of the box.
But the effort was ultimately overturned for a clash between Red Devils shot-stopper David de Gea and Van Dijk in the build-up, with the defender adjudged to have made contact with the Spaniard off the ball.
Former United midfielder Keane, however, blasted the decision to rule out the strike, stating that he felt that the goalkeeper allowed the Dutch international to play into him in order to earn a free-kick.
"It was a huge turning point," the ex-Ireland international told Sky Sports at half-time.
'Why he's disallowed this goal is beyond me. I can't get my head around it. He's got his eye on the ball. De Gea's done this before, I think there's a softness to him. The game's gone mad."
Fellow ex-United man Patrice Evra felt the call was correct, adding: "It's a foul. He's touching De Gea with his head."
Keane however was supported in his beliefs by former Liverpool captain Graeme Souness, who stated: "He's never looked at the goalkeeper, he's got his eyes on the ball.
"Under no circumstances is that a foul. If you’re talking about VAR as some sort of magnificent computer that's perfect in every way, it's human error and they don't know what they're doing, that's the bottom line.
"It's laughable. How much more honest could he be in his challenge?"
Liverpool have now extended their lead at the top of the Premier League to 16 points with a game in hand, as they next face a trip to Wolves in midweek.