West Ham fell victim to a Carling Cup shock as a last minute winner from Daniel Hylton handed League Two Aldershot a famous 2-1 win at Upton Park.
Junior Stanislas put Sam Allardyce's Championship side ahead inside 15 minutes with a thumping drive into the top corner from 25 yards but things fell apart in the second half.
Callum McNaughton was dismissed for bringing down Hylton and Aldershot made their advantage count late in the game.
Luke Guttridge equalised from close range before Hylton settled the tie in the final minute with a shot from inside the area.
Luis Suarez took his goal tally to three goals in as many matches for Liverpool this season as the Reds beat Exeter 3-1 to progress to the third round.
Kenny Dalglish named a surprisingly strong XI at St James Park, featuring the likes of Pepe Reina, Suarez, Charlie Adam, Jordan Henderson and Raul Meireles.
Memories of defeat to Northampton in last season's competition were no doubt still fresh to many Liverpudlians, but they were quickly dispelled thanks to goals from Suarez, Maxi Rodriguez and Andy Carroll.
Meireles' outing didn't last long as he went off with a shoulder injury on 23 minutes, replaced by Carroll, and within moments Liverpool were ahead through Suarez, who drilled home Henderson's deep cross.
Rodriguez found the net, driving home Suarez's cutback as Liverpool's talismanic forward continued to torment the City defence. Carroll was next to get in on the act, slamming home a 25-yard volley, rendering Daniel Nardiello's late penalty - after a foul by Martin Skrtel - mere consolation.
Everton will join Liverpool in the next round, but only after they came from a goal down to beat Sheffield United 3-1.
The Toffees' opening Premier League fixture ended in defeat to QPR on Saturday, but they avoided further agony thanks to a Richard Cresswell own goal, in addition to efforts from Victor Anichebe and Mikel Arteta.
Everton fell behind when Phil Jagielka inadvertently flicked a goal-kick towards his own goal, where Cresswell converted Stephen Quinn's cross. David Moyes' side equalised almost immediately though, after a goalbound effort found the net with the slight aid of a deflection off Cresswell.
By half-time it had become comfortable for the Merseysiders after the excellent Leon Osman set up Anichebe, and then Arteta opened his account for the season with the clincher. Blackburn killed off their match with Sheffield Wednesday inside the opening five minutes at Ewood Park, with Ruben Rochina chalking up a quick-fire brace in a 3-1 victory.
Goals in the third and fourth minutes, one of which was a superb finish, handed Steve Kean's men the ideal start. Wednesday's hospitable defending continued as a poor header let David Goodwillie set his sights in the seventh minute, the new Rovers signing making no mistake. Clinton Morrison grabbed a consolation for Wednesday.
Bolton were almost the shock losers of the evening after they trailed 1-0 at home to Macclesfield for long periods, before eventually winning 2-1.
The opening goal came as a result of hesitancy from Bolton keeper Adam Ogdan, who should have collected a through ball but chose to stay on his line, allowing Emile Sinclair to slot home.
However, Tuncay Sanli found a second-half equaliser for Owen Coyle's side before turning provider for Martin Petrov, who finished well after a classy first touch.
Peterborough proved no match for Middlesbrough, who ran out 2-0 winners at London Road. Marvin Emnes provided the assist for Barry Robson to open the scoring, and then Seb Hines doubled the lead just before the half hour.
The night's other winners were Swindon, who beat Bristol City 1-0 thanks to Raffaele De Vita's goal.