Jurgen Klopp made two changes from the side that beat West Ham United, with Rhys Williams taking the place of Nathaniel Phillips in central defence while Jota started ahead of Roberto Firmino.
After missing good chances in the opening exchanges, Liverpool eventually got the opener in the 16th minute after Jota went through on goal from Trent Alexander-Arnold's pass and kept his composure to chip a delightful shot over goalkeeper Marco Sportiello.
Atalanta were threatening on the break but Jota doubled the lead for Klopp's charges in the 33rd minute after bringing down Joe Gomez's high pass on the left side of the box with his left foot before unleashing a powerful strike past Sportiello at his near post.
Sadio Mane came very close to making it 3-0 for the visitors two minutes later after going through in the centre of the box but Sportiello made a stunning save to keep Gian Piero Gasperini's troops in the game heading into the break.
Liverpool eventually made it 3-0 barely two minutes from the break after Mohamed Salah embarked on lung-busting run from his own half in a counter-attack, and once he got into the box, he turned on his favoured left foot and curled an unstoppable strike into the top corner.
Mane put the game beyond Atalanta with the fourth goal two minutes later with a looping strike over Sportiello, who was off his line after a through ball from Salah.
The Italian side kept on leaving big spaces behind the defence with a high line and Jota completed his hat-trick nine minutes inside the second stanza after going clear on goal from Mane's through ball and rounded Sportiello to score into an empty net.
Duvan Zapata was unlucky not to get a consolation goal for Atalanta in the 62nd minute after going through inside the box, got past Joe Gomez and curled a strike that remarkably came off the inside frame of the goal in the top corner.
Salah had a great chance to make add a sixth goal for the Reds in the last seven minutes after going through on the left side of the box but his low shot across goal was parried away by Sportiello, as the five goals were enough to seal top spot for the Reds.