Newcastle United's surge in form continued as they beat Manchester City 1-0 at St. James' Park with both sides making a number of changes.
Wednesday's EFL Cup results
Aston Villa 1-2 Everton
AFC Bournemouth 2-0 Stoke City
Brentford 0-1 Arsenal
Chelsea 1-0 Brighton
Fulham 2-1 Norwich City
Lincoln City 0-1 West Ham
Liverpool 3-1 Leicester City
Newcastle 1-0 Man City
Despite dominating with 67 per cent of possession, City failed to seriously test the home defence, as they bow out of a cup competition in the third round for the first time under Pep Guardiola.
The only downside to Newcastle's victory was a suspected injury to Isak, who downplayed fears in his post-match interview.
Newcastle's success capped off a good night for most Premier League sides.
Liverpool come from behind to win again
The Reds fell behind in the third minute through Kasey McAteer following a counter-attack.
Szoboszlai made it 2-1 with his second Liverpool goal five minutes after being brought on, before Diogo Jota's improvised finish in the 89th minute sealed the win.
Liverpool, the record holders in the competition with nine successes to their name, have now won seven consecutive fixtures in all competitions and have not lost in 19 matches. They will aim to extend both runs this Saturday against Tottenham Hotspur.
Chelsea claim morale-boosting victory
Prior to the match at Stamford Bridge, the Blues hadn't scored in their previous three encounters.
But Jackson put an end to his and Chelsea's goal drought, sliding the ball into the bottom corner after being played in by Cole Palmer.
The Blues will hope this result proves to be a turning point in their season as they take on west London rivals Fulham next Monday.
However the evening was soured by a hamstring injury to Ben Chilwell, who limped off late on.
Back-to-back wins for Everton
Everton's success was even more impressive, given they had lost 4-0 to Villa in the Premier League in August. It was also their first win over Villa in 10 matches, a run stretching back to March 2016.
One goal enough for Arsenal
Aaron Ramsdale was recalled having been dropped for their last three fixtures in all competitions.
The 25-year-old impressed on his return and produced a crucial second-half save from Yoane Wissa, when he tipped his shot onto a post.
Reiss Nelson's strike proved enough as he capitalised on a poor back pass in the eighth minute.
Arsenal held out for the victory as they extend their unbeaten start to the season to eight matches in all competitions.
Bournemouth score twice in three minutes
Solanke found the bottom corner from Adam Smith's cross, before Rothwell produced an excellent free-kick three minutes later.
The victory was Andoni Iraola's first at home since being appointed earlier this summer as the Cherries book their place into round four for a second successive campaign.
Narrow wins for West Ham and Fulham
The Czech Republic midfielder made a late run into the penalty area to convert from Said Benrahma's corner.
West Ham were fortunate to win though as Lincoln missed a host of chances in the first half, while Lukasz Fabianski denied Reeco Hackett-Fairchild.
Alex Iwobi scored his first goal for Fulham on his first start as they overcame Norwich City 2-1 at Craven Cottage.
The midfielder finished off a team move in the second half that doubled their lead after Carlos Vinicius' close-range finish in the 12th minute.
Norwich reduced the deficit through Borja Sainz, but they could not force penalties.
Next round of the draw
There will be a repeat of last season's final as Manchester United were drawn against Newcastle in the standout fixture for the next round of the EFL Cup.
Elsewhere, Dyche will take on his former side, as Everton face Burnley and there could be a return for Declan Rice when Arsenal travel to West Ham.
Fourth-round ties (selected)
Ipswich v Fulham
Man Utd v Newcastle
Bournemouth v Liverpool
Chelsea v Blackburn
West Ham v Arsenal
Everton v Burnley
The matches will take place the week commencing 30 October.