Simon Mignolet made the crucial save, pawing away a penalty from Stoke’s Marc Muniesa, as Liverpool reached Wembley after an unconvincing display.
Mignolet had earlier saved Peter Crouch’s tame spot-kick but Emre Can struck the post for Liverpool and, with the scores locked at 4-4, it went to sudden death.
Marco van Ginkel and Lucas scored and, after Mignolet’s save, Joe Allen settled matters.
Earlier, Stoke City ended their 57-year wait for victory against Liverpool at Anfield, but Marko Arnautovic’s controversial first-half winner was only enough to take this Capital One Cup semi-final second leg into extra-time.
Arnautovic’s goal, deep into first-half stoppage time, secured a 1-0 win for Mark Hughes’s team to cancel out the home side’s first-leg advantage.
But with neither side able to score in the second half, the two teams were forced to play out an additional 30 minutes in an effort to settle the tie.
Jordon Ibe’s goal in the first leg at the Britannia Stadium had given Liverpool the 1-0 advantage which forced Hughes to go for broke in this return fixture at Anfield.
The Welshman’s game plan was obvious once the team sheets had confirmed the presence of Crouch up front for Stoke, with the former Liverpool and England forward supported by the attacking threat of Walters, Bojan and Arnautovic.
Liverpool’s frailty when defending set-pieces – indeed any aerial ball – had forced Jürgen Klopp to admit that he had held ‘intensive’ talks with his players in order to eradicate the problems that have led to panic whenever the ball has approached Mignolet’s penalty area.
Liverpool tend not to lose at home to Stoke and such was the confidence of the Kop that one banner proclaimed, ‘Anfield South Awaits.’
When Liverpool won four successive League Cups in the 1980s, Wembley was every inch Anfield South due to the regularity of the club’s trips there to major finals, but Klopp’s team went into this game with trophies in thin supply in recent years.
Two unsuccessful semi-finals last season, with defeats against Chelsea in this competition and Aston Villa in the FA Cup, only served to increase the frustration of a club that has become desperate to recreate the magic of their glory days.
Klopp had insisted he had no interest in last season’s disappointments, claiming that his reign is all about the here and now, but there is nothing like winning silverware to make the future a better place and the German had urged Anfield to unleash “the power of LFC” to get his team to Wembley.
Stoke have proven their ability to beat the best this season, with Manchester City, Chelsea and Manchester United all falling victim to Hughes’s team at the Britannia, but their form has been less convincing away from home.
So it was perhaps unsurprising that they struggled to test Liverpool during a scrappy first half, with Crouch nullified by Kolo Touré and Mamadou Sakho.
Stoke seemed caught between two stools. They had the towering Crouch to torment Liverpool in the air, but the ball barely left the ground, so determined were Bojan and Arnautovic to make a difference with flair rather than punts upfield.
Chances were few and far between. Walters saw an early shot from 20 yards deflected behind by Milner, before the Republic of Ireland forward, born across the Mersey on the Wirral, flashed a left-footed effort wide of Mignolet’s far post after running onto an Erik Pieters pass and escaping the attentions of Sakho.
Liverpool, with Benteke once again named on the bench, were happy to sit back and contain Stoke. But the two chances which came their way before half-time fell to midfielder Emre Can – the first a drag-back and shot from 20 yards which flew high and wide before the German fizzed a right-footed strike inches wide from 25 yards.
Stoke made the breakthrough in first-half stoppage time, though, with a goal that should not have been allowed as Arnautovic appeared to be at least a yard offside when he was released by Bojan.
Hughes’s team had at least sensed the chance to catch Liverpool off guard, breaking with a swift counter-attack as the home side waited for referee Jon Moss to blow the whistle for half-time.
But when Walters fed Bojan on the right, Arnautovic had already raced ahead of Touré and Sakho into the penalty area.
The Austrian failed to halt his run and the assistant referee’s flag should have been raised as soon as Bojan played the ball, but the flag did not move and, as Liverpool’s bewildered defenders appealed for offside, Arnautovic guided a right-foot strike past Mignolet in front of the Kop.
It was a key error by the linesman, but it gave Liverpool something to rail against in the second half and they began with a sense of injustice, desperately attempting to cancel out Stoke’s lead.
Roberto Firmino struck the foot of the post with a right-foot volley on 48 minutes, but as the volume inched higher inside Anfield, it was the visitors who grew in stature.
And but for two crucial defensive blocks by Sakho – both from Walters – Stoke would have deservedly doubled their lead inside the opening 15 minutes.
Liverpool simply could not generate a head of steam and the frustration grew within Anfield as Stoke grew more and more composed.
Hughes’s players were more at ease on the ball, more willing to create and Liverpool began to pound long balls forward in an effort to find the goal which would take them to Wembley.
Sakho, who had been heroic at the back, burst forward in an attempt to make a difference, but headed a Milner cross over.
Then came the moment when Benteke somehow failed to connect with Moreno’s cross, six yards from goal.
The ball appeared perfectly weighted for the Belgian to power into the net, but he ducked at the vital moment, leaving Jon Flanagan to stumble on the ball.
It was chaotic and shambolic at the same time, and somehow summed up Liverpool’s performance.
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