Match ends, Liverpool 2, Brighton and Hove Albion 1.
Liverpool keeper Alisson was sent off for a blatant handball outside his penalty area as the Reds moved 11 points clear at the top of the Premier League with victory over Brighton.
Jurgen Klopp's side were coasting to victory after two Virgil van Dijk headers from Trent Alexander-Arnold assists in the space of six first-half minutes.
But Alisson's red card - for handling as Brighton substitute Leandro Trossard bore down on goal - gifted the visitors a lifeline.
Substitute Adrian's first touch was to gather the ball out of his own net after Lewis Dunk's cute free-kick left the keeper - who was still organising his wall - stranded, before Liverpool's stopper saved late on from Aaron Mooy.
Earlier in the day, defending champions Manchester City were held to a 2-2 draw at Newcastle United.
Leicester City will cut Liverpool's lead to eight points if they beat Everton on Sunday (16:30 GMT).
Liverpool do it the hard way
Victory means Liverpool have equalled their longest ever unbeaten run in the top flight, having also gone 31 games without defeat between May 1987 and March 1988.
Yet this was anything but straightforward for the leaders as Alisson became the first Reds keeper to be sent off in a Premier League game since fellow Brazilian Doni in 2012.
With his side 2-0 up and closing in on three points, Alisson came rushing out of his penalty area to handle the ball as Brighton attacked.
As a result, Alisson will now miss the Merseyside derby with Everton at Anfield on Wednesday.
His actions set up a nerve-wracking finale and Dunk's free-kick - an awful goal to concede from Liverpool's point of view - means Klopp's side are still without a clean sheet since 28 September.
Adrian saved his side by keeping out Mooy as mid-table Brighton piled forward in search of an equaliser.
The Reds had looked like coasting to victory after Van Dijk's double, and Brighton keeper Mat Ryan made three fine saves to frustrate Roberto Firmino, twice, and Mohamed Salah.
Liverpool head into a demanding December, a month during which the club will play nine fixtures in four different competitions, with a fifth successive league win - but this was far too close for comfort.
Spirited Brighton give leaders a scare
Brighton slipped to 15th in the table after a third straight defeat, but there are grounds for optimism before a busy December programme.
In a week during which Seagulls boss Graham Potter extended his contract to 2025, his side gave the leaders a real scare even before the hosts were reduced to 10 men.
Dunk went close from a Pascal Gross corner before scoring his second goal in as many games, while teenage forward Aaron Connolly also showed flashes of real promise.
With his side trailing 2-0, the 19-year-old managed to create space for himself inside Liverpool's penalty area and test Alisson despite close attention from Dejan Lovren and Van Dijk.
One worry for Brighton is their defending from set-pieces as Van Dijk was allowed to dominate the aerial duels. That will be a real concern for Potter with matches against Arsenal, Tottenham and Chelsea on the horizon.
Man of the match - Virgil van Dijk (Liverpool)
'Lots of positives' - what they said
Liverpool boss Jurgen Klopp: "It was unnecessary [for the game to be nervy at the end], of course, because we had unbelievable chances. Their keeper made some good saves.
"It was difficult this game because Brighton are a good football side. They had a lot of possession and we had to work really hard.
"I loved that the boys were prepared to do that after a busy week."
Brighton boss Graham Potter: "There were lots of positives for us. In the first 10-15 minutes we weren't quite as aggressive and didn't have the belief we needed.
"We gave a really good account of ourselves against a top team. We are disappointed because we came away with nothing but with the performance and the effort, we could have come away with something.
"We had good chances at 2-0 down. Virgil van Dijk was so powerful in his two actions for their goals and we weren't as good. That's the reality.
"But over the 90 minutes we put so much into the game and we need to take that forward and carry on improving."
Brighton skipper Lewis Dunk: "To come here and be disappointed speaks volumes. There's so much to move forward with and at times we were excellent.
"The game was decided by the first 15 minutes, but not many teams will come here and feel like this."
Why Alexander-Arnold is the assist king - the stats
- Since the start of last season, no player has provided more Premier League assists than Liverpool full-back Trent Alexander-Arnold (17).
- Brighton have lost nine of their 11 away league games against Liverpool, with their only victory coming in the top flight in March 1982.
- Brighton are without a win in their past six away Premier League games - losing each of the past four.
- Liverpool have registered 14 consecutive home wins in the Premier League, their second longest home top-flight winning run behind a 21-game streak between January-December 1972.
- Since the start of last season, Liverpool defender Virgil van Dijk has scored more Premier League goals than any other defender (7).
- Liverpool have scored 40 Premier League goals via set-pieces (including penalties) since August 2018, the most of any side in this period.
- The Reds are unbeaten in each of their last 98 Premier League games at Anfield when leading at half-time since losing to Arsenal in December 2009.
There's a busy midweek of Premier League action coming up with Liverpool hosting neighbours Everton on Wednesday (20:15 GMT), while Brighton are at Arsenal on Thursday (20:15).
- 1AlissonBooked at 76mins
- 4van Dijk
- 15Oxlade-ChamberlainSubstituted forAdriánat 78'minutes
- 11SalahSubstituted forLallanaat 69'minutes
- 9FirminoSubstituted forOrigiat 76'minutes
- 22MontoyaSubstituted forAlzateat 69'minutes
- 8BissoumaSubstituted forTrossardat 69'minutes
- 44ConnollySubstituted forMaupayat 76'minutes
- Martin Atkinson
- Shots on Target
Second Half ends, Liverpool 2, Brighton and Hove Albion 1.
Foul by Dan Burn (Brighton and Hove Albion).
Dejan Lovren (Liverpool) wins a free kick in the defensive half.
Offside, Brighton and Hove Albion. Leandro Trossard tries a through ball, but Neal Maupay is caught offside.
Attempt saved. Pascal Groß (Brighton and Hove Albion) header from the centre of the box is saved in the centre of the goal. Assisted by Steven Alzate with a cross.
Attempt saved. Aaron Mooy (Brighton and Hove Albion) right footed shot from outside the box is saved in the bottom right corner. Assisted by Leandro Trossard.
Offside, Brighton and Hove Albion. Dale Stephens tries a through ball, but Neal Maupay is caught offside.
Attempt missed. Dan Burn (Brighton and Hove Albion) left footed shot from the left side of the box is high and wide to the left. Assisted by Aaron Mooy with a headed pass.
Attempt blocked. Davy Pröpper (Brighton and Hove Albion) right footed shot from outside the box is blocked. Assisted by Pascal Groß.
Goal! Liverpool 2, Brighton and Hove Albion 1. Lewis Dunk (Brighton and Hove Albion) from a free kick with a right footed shot to the bottom left corner.
Substitution, Liverpool. Adrián replaces Alex Oxlade-Chamberlain.
Alisson (Liverpool) is shown the red card.
Hand ball by Alisson (Liverpool).
Attempt blocked. Leandro Trossard (Brighton and Hove Albion) right footed shot from outside the box is blocked. Assisted by Adam Webster.
Substitution, Brighton and Hove Albion. Neal Maupay replaces Aaron Connolly.
Substitution, Liverpool. Divock Origi replaces Roberto Firmino.
Foul by Dale Stephens (Brighton and Hove Albion).
Adam Lallana (Liverpool) wins a free kick in the defensive half.
Substitution, Brighton and Hove Albion. Steven Alzate replaces Martín Montoya.