Liverpool cruised into the League Cup third round with a 3-1 win over Exeter City, while fellow Premier League sides Everton, Blackburn Rovers and Bolton Wanderers also avoided early exits.
Kenny Dalglish's team were playing in the second round of the competition for the first time since 1999 following a rare failure to qualify for any European event. But the seven-time League Cup winners were never in danger of crashing out to a embarrassing defeat at St James' Park as goals from Luiz Suarez, Maxi Rodriguez and Andy Carroll gave Dalglish his 200th win in all competitions over two spells as Liverpool manager.
Dalglish made eight changes to the team that won 2-0 at Arsenal on Saturday, but was still able to name a strong line-up including Suarez, Jordan Henderson, Charlie Adam and Pepe Reina.
Liverpool lost Raul Meireles to an early shoulder injury, but the Reds took the lead in the 23rd minute when Artur Krysiak could only tip Henderson's cross to Suarez, who volleyed home despite Richard Duffy's attempt to clear.
Rodriguez got the second goal when he converted a Suarez pass in the 55th minute and substitute Carroll scored from the edge of the area three minutes later. Exeter grabbed a consolation goal in the 80th minute when Martin Skrtel tripped Daniel Nardiello and the striker picked himself up to score the resulting penalty.
Everton lifted some of the gloom around Goodison Park with a 3-1 win over Sheffield United.
David Moyes' men made a miserable start to their Premier League campaign, losing 1-0 at home to QPR on Saturday just days after chairman Bill Kenwright admitted there is no money to spend on signings as the club's bank has stopped providing fresh funds.
Another bad day looked likely when Richard Cresswell gave the Blades the lead in the 28th minute, but the United striker deflected Jack Rodwell's shot into his own net three minutes later. Victor Anichebe finished off Ross Barkley's shot in the 37th minute and Spanish midfielder Mikel Arteta struck with a curler five minutes later.
Blackburn eased a little of the pressure off coach Steve Kean with a 3-1 victory over Sheffield Wednesday at Ewood Park. Kean was beginning to feel the heat after Rovers lost their opening two Premier League matches and could not afford a shock defeat against today's opposition.
Rovers scored three times in the first seven minutes as Spanish forward Ruben Rochina netted with two clincal strikes before David Goodwillie bagged his first goal following his move from Dundee United.
Bolton come back
Turkish forward Tuncay Sanli scored on his debut as Bolton came from behind to beat League Two outfit Macclesfield 2-1.
There is a gap of 75 league places between the teams, but Macclesfield took the lead in the 11th minute when Tony Diagne's through-ball sent Emile Sinclair clear to slot home. Bolton equalised through Tuncay's volley in the 56th minute, though, and the Turk then turned provider in the 73rd minute as his pass was buried by Martin Petrov.
Peterborough demolished Ipswich 7-1 on Saturday, but Darren Ferguson's side found it much harder against fellow Championship team Middlesbrough, who strolled to a 2-0 win at London Road.
Ten-man West Ham United were booed off after the Championship side suffered a shock 2-1 home defeat against Aldershot in a delayed first round tie, with Danny Hylton scoring an 89th minute winner for Dean Holdsworth's League Two team.
Bristol City, also of the Championship, fared no better against League Two opposition as Paolo Di Canio's Swindon won 1-0 at Ashton Gate in another first round match.