It was a lively atmosphere at Elland Road with Marcelo Bielsa's side looking to take the impetus to the Reds, with Alisson forced into an early save from Raphina.
But Liverpool looked impressive and did their utmost to quieten the crowd, with Mohamed Salah looking particularly sharp down the right as the Reds looked to put pressure on the Leeds backline.
They looked favourites to make the breakthrough and they did just that in the 20th minute as Trent Alexander-Arnold's drilled ball was prodded into the back of the net by Salah, who reached the milestone of 100 Premier League goals in the process.
The Reds had a handful more chances in the first half to double their advantage, including having a Thiago header ruled out for offside and Sadio Mane, Harvey Elliott and Virgil van Dijk all coming close.
VAR ruled in Leeds' favour when Mane found himself through on goal and was thwarted by a challenge before getting his shot off. But it didn't take soon after for the Reds to double their lead.
Van Dijk rose highest from a Liverpool corner and nodded the ball down into the path of Fabinho, who saw his effort blocked before he eventually prodded the ball into the back of the net from the rebound to make it 2-0 and put Liverpool in complete control.
But what was a successful afternoon at the office for Liverpool thus far was marred by a serious injury to Elliott, who was the recipient of a robust challenge from red-carded Pascal Struijk.
The Reds youngster was stretchered off the pitch after receiving treatment for over four minutes, with several of Liverpool's squad looking on in dismay at what is more than likely an extremely serious injury.
Liverpool continued to mount pressure on the hosts as the half wore on, with substitutes Jordan Henderson and Alex Oxlade-Chamberlain both threatening. But the bulk of the chances landed at the feet of Mane, who was unable to turn the ball home on more than one occasion.
But the Senegalese finally found his goal in the eight minutes of added time as Thiago controlled Henderson's cross into the box and squared the ball to Mane, who swivelled and smashed the ball into the back of the net to round off a 3-0 win for the Reds.