League Cup: Bernd Leno saves two penalties as Arsenal beat Liverpool in shootout to reach quarter-finals
Leno, who also kept a clean sheet through 90 minutes as the game ended 0-0, blocked penalties from Divock Origi and Harry Wilson.
Williams was criticised online after losing possession in the build-up to Lincoln's first goal during Liverpool's 7-2 League Cup win last week.
League Cup: Manchester City, United breeze past Burnley, Brighton to reach quarter-finals; Everton also advance
Guardiola's men would have won by an even bigger scoreline but for a fine display from Burnley keeper Bailey Peacock-Farrell.
League Cup: Jose Mourinho gets better of Frank Lampard as Tottenham see off Chelsea to reach quarter-finals
Going out of the League Cup was the latest setback for Lampard, whose side has only four points from its opening three Premier League games.
Tottenham Hotspur host Chelsea in the League Cup fourth round on Tuesday before a final Europa League qualifying tie at home to Maccabi Haifa just 48 hours later.
League Cup: Tottenham to face Chelsea in fourth round after being awarded bye due to COVID-19 outbreak at Leyton Orient
Tottenham will now host Chelsea on Tuesday in the fourth round in a run of three home games in three different competitions across five days
Liverpool will face Arsenal twice at Anfield in three days next week after Jurgen Klopp's much-changed side hit Lincoln for seven with Takumi Minamino and Curtis Jones both scoring twice.
League Cup: Hat-trick for Kai Havertz as Chelsea stroll past Barnsley; wins for Arsenal, Newcastle, Everton
Kai Havertz — signed for $92 million — announced himself in English football by scoring a first career hat-trick in Chelsea's 6-0 win over Barnsley in the third round of the League Cup
League Cup: Manchester United, West Ham advance to fourth round as multiple coronavirus cases cause chaos
In United's first meeting with Championship side Luton since 1992, boss Ole Gunnar Solskjaer made 10 changes, giving full debuts to goalkeeper Dean Henderson and close-season signing Donny Van De Beek.
League Cup: Tottenham's fixture against Leyton Orient postponed after string of COVID-19 cases at League Two club
Just two hours before Jose Mourinho's side were due to play the third-round match at the Breyer Group Stadium, the English Football League announced it had been postponed.
City, who have won the League Cup for the past three seasons, start the defence of their trophy against Bournemouth on Thursday and Guardiola knows they cannot afford to lose more players.
League Cup: Jacob Brown's late goal helps Stoke City beat Wolves; Burnley overcome Sheffield United on penalties
Brighton were comprehensive 4-0 winners over Portsmouth with Alexis Mac Allister, Alireza Jahanbakhsh, Bernardo and Victor Gyokeres on target.
League Cup: Premier League clubs Leeds, Southampton crash out of tournament; Everton thrash Salford City
Southampton boss Ralph Hassenhuttl named a strong side at St Mary's but still got no response from their disappointing start to the season at Crystal Palace on Saturday.
The Premier League will open one month later than usual because of the July finish to its delayed 2019-20 campaign, and the UEFA competitions continuing to 23 August.
League Cup: Manchester City ride on Sergio Aguero, Rodri's goals to lift trophy for third consecutive season
Manchester City became the first side to win the competition three seasons in a row since Liverpool claimed four straight titles from 1981 to 1984.
League Cup: Trezeguet fires late winner to guide Aston Villa into final with win over Leicester City
Aston Villa’s Trezeguet struck a dramatic 93rd-minute winner to send them into the League Cup final with a 2-1 victory over Leicester City that gave them a 3-2 aggregate win on Tuesday.
League Cup: Manchester United boss Ole Gunnar Solskjaer urges players to produce 'perfect performance' in semi-final second leg against City
United trail 3-1 from the first leg of the semi-final at Old Trafford as they prepare to face their local rivals in the return leg at the Etihad Stadium on Wednesday.
Premier League: Leicester City's Wilfred Ndidi ruled out till February after sustaining knee injury, confirms Brendan Rodgers
Ndidi has been crucial to Leicester’s fortunes this season and the influential Nigerian leads the Premier League in both tackles and interceptions.
League Cup: Manchester City boss Pep Guardiola explained strategy for United match in just 15 minutes, says Kevin De Bruyne
Guardiola opted to play without a recognised striker at Old Trafford, giving De Bruyne and fellow midfielder Bernardo Silva licence to push forward centrally and the move worked perfectly as City scored three times before halftime
League Cup: Aston Villa defender Ezri Konsa's 'farcical' moment sees Leicester rescue semi-final first-leg draw
Leicester, second in the league and the big pre-match favourites to win their semi-final, had 21 shots to Villa's three but struggled for fluidity in front of the visitors' stacked defensive line