In front of British and Commonwealth boxing champion David Price, Liverpool finally managed to land a knockout blow. But for Brendan Rodgers, it has probably come too late to salvage a shot at glory.
Price, a lifelong Liverpool fan, was paraded on the Anfield pitch at half-time ahead of a fight against American Tony Thompson at the city's Echo Arena next Saturday. His aim is to move a step closer to a world title fight against Wladimir Klitschko. While his star is in the ascendant, Rodgers' pursuit of success has proved rather more troublesome.
This has been a sobering week for Liverpool's manager, with a home defeat against West Brom on Monday wrecking his hopes of Champions League qualification, and a loss to Zenit St Petersburg on Thursday severely denting his chances of winning the Europa League.
Rodgers has a sporting metaphor of his own to describe his first eight months in charge at Anfield, saying: "I've likened us to a marathon runner in the group, getting ready to make a move for the finish line. We're ready to make a run, and then we trip up. But we trip ourselves up. We have to change that."
Overall, it was a satisfying afternoon for Rodgers. Philippe Coutinho, the £8 million January signing from Inter Milan, marked his full debut with a goal and left to a standing ovation after an hour. His side created enough chances to have hit double figures, and they kept a first clean sheet in six matches. On the downside, striker Fabio Borini's injury-plagued season appears to have been ended three months early by a dislocated shoulder suffered in the closing stages.
"He will probably be out for the season," Rodgers said. "He's unfortunate. He's had a similar injury before when he was at Chelsea, but it was his other shoulder."
Otherwise, Rodgers could smile. In fact, even Luis Suarez's rather stroppy reaction to being substituted with 13 minutes to go did not spoil his mood, with the Northern Irishman, who was keen to keep him fresh for Thursday's Europa League return against Zenit, adding: "That's the nature of him. He's a wonderful competitive character. He wants to play every minute, and I would never want to take that away from him."
Victory over Swansea, the club he left to move to Anfield last June, improved his mood after a few days of disappointment. Yet although it was a big win, it was hardly a heavyweight triumph. Swansea were overcome comfortably, but they looked for all the world a team with other things on their mind.
Michael Laudrup's side demonstrated their commitment to the Capital One Cup in October with a thoroughly deserved 3-1 victory at Anfield. On their return to Merseyside's red corner, Laudrup demonstrated his commitment to the competition again.
Next Sunday's Wembley final against League Two side Bradford offers Swansea the chance of a first-ever major trophy, and of European qualification secured by February. It is, for Laudrup, too good an opportunity to miss. It showed in his Anfield team selection.
His 15-goal top scorer Michu was left on the bench to keep him fresh for Wembley, as was centre-back Ashley Williams, whose fitness could not be risked with Chico Flores already set to miss the final with an ankle injury.
In all, Laudrup made seven changes to the side who dismantled QPR 4-1 a week ago. His team played like strangers. At times in the second half, they were in danger of matching the 8-0 defeat suffered at Anfield in a 1990 FA Cup third-round replay. Goalkeeper Michel Vorm spent long periods locked in one-to-one combat with Liverpool striker Daniel Sturridge. It was feeble stuff.
"We could have lost seven or eight-nil easily, had it not been for Michel," Laudrup said. "That's not good enough."
For Rodgers, though, this was a breakthrough of sorts. For the first time as Liverpool's manager, he was able to engineer a victory over a team in the top half of the Premier League. In doing so, he lifted his current club above his former one in the table.
It was a win bookended by two penalties, the first converted by Steven Gerrard, the second by Sturridge. In between, there was an extraordinary 11-minute spell at the start of the second half in which Coutinho, Jose Enrique and Luis Suarez all scored, and Liverpool opened up holes in Swansea's defence at will.
There were a fair few missed chances as well – a common theme for Liverpool of late. With the game at 0-0, Suarez hit the bar with an ambitious dipping shot, Sturridge headed over from a Stewart Downing cross and Coutinho somehow screwed a close-range effort into the advertising boards.
But while profligacy had proved costly against West Brom and Zenit, it did not matter here. When Kemy Agustien gave Suarez a nudge inside the area, linesman Mike Mullarkey raised his flag to his chest and referee Howard Webb pointed to the spot. Gerrard, who has seen a penalty saved in front of the Kop against West Brom, slotting his spot-kick into the opposite corner and got the opposite result. Liverpool did not look back.
Brazilian Coutinho strode through a static Swansea defence to score less than 30 seconds after the interval, then Enrique finished a beautiful passing move by firing a shot high into the net, before Suarez collected Downing's pass and evaded two Swansea defenders to steer a shot into the corner. Sturridge got the goal his performance deserved when he converted a second penalty, given when substitute Wayne Routledge handled Enrique's crossfield pass.
It felt as if Liverpool had discovered the ruthless streak that has made Price a success in the world of boxing. They will need to keep showing some of his drive as well.
Interviewed on the pitch at half-time, Price was asked about the likelihood of a world-title fight against Klitschko. "If I keep working hard, there's no reason why I can't get there," he replied. It is a motto that will serve Rodgers well in his chase for glory at Anfield.
MAN OF THE MATCH: Daniel Sturridge. Liverpool have looked a far more dangerous side since the striker arrived from Chelsea in January, and his understanding with Suarez and new arrival Coutinho could yet turn into something special. The striker should have scored long before he did, but his ability to get into the right positions promises much.
LIVERPOOL VERDICT: Brendan Rodgers talked afterwards of a plan to dominate possession in the first half and drive their advantage home in the second. They were able to do that with little difficulty, but will face far sterner tests than this over the remainder of the season, starting with the Europa League last-32 second leg against Zenit St Petersburg on Thursday.
SWANSEA VERDICT: Michael Laudrup's post-match reaction suggested that he felt this was his team's worst performance of the season. It would be hard to argue. This was a listless display from a group of largely fringe players, who did nothing to press their case for regular inclusion.