The Reds went ahead through Sadio Mane, as he raced on to James Milner's pass to slot past Kasper Schmeichel, putting Liverpool on course for another win.
Leicester – managed by ex-Liverpool boss Brendan Rodgers – hit back late on as James Maddison equalised from Ayoze Perez's pass, but there was a late, controversial twist.
Mane went down under Marc Albrighton's injury-time challenge, and despite Leicester claiming he dived, the penalty was given, and Milner stepped up to score.
Leicester gave Liverpool a run for their money, but the Reds battled through to win, and with Manchester City losing to Wolves on Sunday, the Reds now already have an eight-point lead at the top of the Premier League table.
Liverpool fans will have been celebrating the win, but it also seems that many of them were impressed with Leicester's goalscorer Maddison on Saturday afternoon.
The 22-year-old is one of the top playmakers in the Premier League, and with Liverpool's midfielders more workmanlike than creative, some really want Maddison to join Jurgen Klopp's side.
Maddison took to Twitter to react to the defeat, but was bombarded with messages from Liverpool fans telling him to join the Reds in 2020.
Some suggested they will see him in a red shirt at Anfield very soon, even telling him that Anfield suited him after a strong display, but whether Klopp actually moves for the Englishman remains to be seen.
Well done on your audition yesterday mate, Anfield suits you. See you in January— Josh (@LFCJosh23) October 6, 2019
You definitely deserved something from the game. Sure when sign for us next season you will get plenty of points at Anfield.— Belfastkop (@thebelfastkop) October 6, 2019
See you back at Anfield in January in a Liverpool shirt!! Lol— David Lewis (@scouselad01) October 6, 2019
Come to Liverpool Maddersss— ፬ኪሎ (@YifelaBuna) October 5, 2019
Don't worry champ. You'll be on the winning side come next summer— Aditya Rane (@adiji) October 5, 2019
See u in the summer mate— Aaron (@AaronLFC6) October 5, 2019
Good game James. We would welcome you at Anfield— Leigh (@LeighBergin) October 5, 2019
come to liverpool— صهيب (@Sou_haib_) October 5, 2019
Good Performance mate see you in the summer— . (@abxlxo13) October 5, 2019
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