The hosts took the lead before 15 minutes when Start Dallas was whistled for handball and Mohamed Salah calmly dispatched the ensuing spot kick to make it 1-0.
Salah then set up Joel Matip for Liverpool's second with a deft pass into the area following a slick team move, before adding his second of the night -- once again from the penalty spot -- after VAR determined Sadio Mane had been tripped in the area.
Liverpool, who took their Anfield league goal tally to 50 for the season with the second penalty, should have had at least one more before the break, with Fabinho and Salah both missing clear-cut openings.
Jurgen Klopp's side came out of the dressing room after half-time with a 3-0 lead and continued to apply non-stop pressure on the Leeds defence. The pressure told as the second half wore on with Mane adding a pair of late goals before Virgil van Dijk struck to reach the final scoreline.
"I think for people outside it is better to have three or six-point gap than to have a 20 or 30-point gap, so it is more exciting," Klopp told the BBC. "But we have to win a lot of the games against all the difficult opponents and that will be a tricky task. We will give it a try."
Coming into the match, Leeds had conceded at least twice in each of their last five away league games, having also shipped four at home to Manchester United on Sunday.
"Two different teams in class," Leeds midfielder Adam Forshaw said. "It is difficult coming to a place like this but we are missing big players, we have missed them through the season.
"Tonight feels like the end of the world but we are still in an okay position, we can't feel sorry for ourselves."
Salah reached a notable milestone in the match, surpassing Chelsea legend Didier Drogba for the most goal contributions by an African player in Premier League history with 116 goals and 44 assists. Drogba totalled 104 goals and 55 assists in his illustrious career.
Liverpool are now on 60 points after 26 games, three behind Man City, who lost to Tottenham Hotspur on Saturday, while Leeds remain in 15th place with 23 points from 25 games.
Given how close Liverpool and City are, the title could be decided on goal difference and this result will do Klopp's side a world of good in that regard.