The impressive Foxes took just four minutes to draw first blood through Kiernan Dewsbury-Hall, but Faes turned into his own net twice before the break to settle an energetic contest.
In doing so, Faes followed in the footsteps of Michael Proctor, Jonathan Walters and Jamie Carragher - the other three players to score multiple goals in one Premier League game - but the wasteful Reds could count themselves fortunate as Leicester also failed to make periods of attacking promise pay.
Exposing the Liverpool high line and Fabinho-less midfield, Leicester players put the ball in the back of the net three times in the first half, but only one of them came at the correct end of the field.
With no more than four minutes on the clock, Dewsbury-Hall was given free rein to run straight through the Liverpool defence after a neat flick from Patson Daka, with Jurgen Klopp's engine room simply non-existent.
Dewsbury-Hall's shot into the ground went over Alisson Becker into the back of the net to silence the Anfield crowd, who were not blessed with excellence from those in red, as the hosts struggled to cope with Leicester's effective pressing and balls over the top.
The Foxes' momentum was briefly disrupted by a 15th-minute injury to Daka, and Danny Ward barely had a save to make, although he was thanking his lucky stars for the offside flag after a poor attempt at a clearance allowed Mohamed Salah to fire home in the 26th minute.
In the 38th minute, ex-Liverpool man Ward would make his voice heard across Merseyside when shouting to claim a Trent Alexander-Arnold cross, but Faes instead stuck a sliding leg out and helplessly watched the ball loop over the Leicester keeper into the back of the net.
Undeniably against the run of play, Liverpool were level, and just four minutes later, Faes would comically channel his inner Carragher to join the exclusive club of players to score multiple own goals in a Premier League game.
The lively Darwin Nunez was played through by Alex Oxlade-Chamberlain, and even though the wasteful Uruguayan's chipped effort came back off the post, Faes was on hand to inadvertently poke home the rebound into the roof of the net to put Liverpool ahead.
Immediately after the break, Liverpool had an itch to put the ball in the back of the net themselves for the first time on the night, with Jordan Henderson sending a half-volley just wide in the 51st minute before Mohamed Salah dragged an effort the wrong side of the far post two minutes later.
Brendan Rodgers's side - led by the effervescent Dewsbury-Hall - continued to show signs of life in the final third, and the Englishman ghosted in to meet Timothy Castagne's cross with a free header in the 61st minute, but he got his connection all wrong and wasted a golden opportunity.
A lack of a killer final ball bedevilled both sides in the final 30 minutes, although there was time for the perennially profligate Nunez - whose all-around play still made him a menace - to miss a few second-half chances.
Liverpool clung on for a narrow triumph which moved them to within two points of the top four, while Leicester remain 13th after suffering back-to-back defeats since the World Cup.
Klopp's outfit now prepare to take on Brentford in their opening game of 2023 on Monday, while the Foxes host Fulham a day later.