The Belgian centre back miscued a clearance in the 38th minute to hand Liverpool the equaliser, after Leicester took a surprise fourth minute lead through Kiernan Dewsbury-Hall, and then put the ball into his net again on the stroke of halftime.
Liverpool, who stay sixth but move within a point of fifth-placed Manchester United, albeit having played a game more, will consider themselves lucky after a stuttering performance with both clubs guilty of missing good chances.
"We are here to get results and that’s what we did tonight," said Liverpool manager Jurgen Klopp, whose side have now won four league games on the trot.
"But we lose balls at the wrong moments and we were too open at times. We have to take the result momentum but have to play better in our next match against Brentford."
Leicester remain 13th, four points above the relegation zone, after they lost a 10th league game of the season.
They had grabbed the lead as Liverpool were caught out by a long clearance from goalkeeper Danny Ward, followed by two quick touches that put Dewsbury-Hall away on goal.
He ran almost half the length of the pitch, outpacing the defence, to score.
Leicester looked good value for their advantage until Faes’ miscued clearance of a ball into the box from Trent Alexander Arnold looped up over Ward into the back of the Leicester net from a tight angle.
Faes was under no pressure as he attempted to hack the ball clear, giving away a cheap, although unfortunate, equaliser.
He was also unlucky with Liverpool’s second seven minutes later, chasing back as Darwin Nunez’s chipped effort hit the Leicester post and rebounded back into play, hitting the onrushing Faes on the knee and flying into the net.
"He has come back a bit rusty, not playing at the World Cup with Belgium, and it’s going to take him time to get back to speed. But he’s also been fantastic for us this season. It was unfortunate for him tonight," said Foxes boss Brendan Rodgers.
Liverpool’s Mohamed Salah had three second half chances to increase the home side’s lead while Nunez came close with an effort that whistled over the bar with 12 minutes left.
Leicester, who lost 3-0 at home to Newcastle United on Boxing Day in their first league game back after the World Cup break, also created some decent chances, notably for Harvey Barnes who tormented Liverpool down the left-hand side.
He hit the woodwork in the last 10 minutes but Leicester were offside in the build-up.
Liverpool, who have 28 points from 16 games, are away at Brentford on Monday while Leicester, on 17 points from 17 matches, next host Fulham on Tuesday.