Liverpool were simply too clinical and professional for a famous upset to ever realistically be on the cards and by the end, with the match over as a contest, the visitors were threatening to make this a more humiliating experience than a refreshingly sprightly Bournemouth deserved.
Bournemouth were so impressive in the first half that Brendan Rodgers was compelled to criticise Liverpool for not working hard enough afterwards and, with a touch more composure in the final third, they might have had more to show for their fearlessness. That was the crucial difference between the sides, though. Bournemouth defended well and attacked vigorously, but Brad Jones did not have to make a notable save until the final minutes, pushing Lewis Grabban's drive over, and although Liverpool were below their best, they were ruthless enough to reach the fifth round of the FA Cup thanks to goals from Victor Moses and Daniel Sturridge.
Rodgers admitted that this was the sort of game that Liverpool might have lost last year and he was right, because they did: they lost to Oldham Athletic in this round last season. That defeat represented a nadir for Rodgers and Bournemouth, 16th in the Championship and a division above Oldham, had to be taken seriously if Liverpool were not to suffer more embarrassment. Steven Gerrard, Sturridge and Luis Suárez all started, even though Everton visit Anfield on Tuesday. "We're a very thin squad and we've got a number of injuries but the tradition of Liverpool in the FA Cup is huge and we want to respect that," Rodgers said.
Whereas Liverpool were roughed up by Oldham's physicality, Bournemouth presented them with a more cerebral challenge. They wanted to pass Liverpool off the pitch, not kick them off it, even if Martin Skrtel did end the match with a bandaged head after an accidental collision. Such is the influence of their manager, Eddie Howe, whose philosophy is admired by Rodgers.
"When you have a team that wants to play football they're the most courageous players on the field," Liverpool's manager said. "I don't think it's too nice. It's easy to coach a team to sit back and then pump the ball up the pitch. Don't think it's too nice. In this country, it's deemed too nice but that's why we cry when we get to the World Cup and we're not technically good enough."
The problem for Bournemouth was the absence of a cutting edge. They were the better side before the break, passing crisply and moving intelligently, and Andrew Surman twice went close. He sent an early header wide and then saw Kolo Touré deflect a goalbound effort wide, while Harry Arter brushed the side-netting with a shot from the edge of the area.
Yet Liverpool took the lead with their first worthwhile attack. After a Bournemouth move fizzled out after 26 minutes, Liverpool countered with ominous intent on the right and when Suárez's cross-field pass found Victor Moses, the winger cut inside and drilled a low shot from 18 yards past Lee Camp, who was too slow to get down at his near post. Moses's celebration was decidedly and surprisingly muted. "He's quite laidback," Rodgers explained of a player who has not lived up to expectations while on loan from Chelsea.
In the blink of an eye, Liverpool were in front and the lead should have been extended after 38 minutes when Bournemouth made a dog's dinner of a clearance, allowing Suárez to tee up Jordan Henderson, who blazed over from the penalty spot.
Liverpool were fortunate when the hosts' Simon Francis was put through and was just about to pull the trigger when he appeared to have his shirt pulled by Martin Kelly. He fell to ground but the referee Lee Probert gave nothing.
This was one of Suárez's less potent games, yet it was still telling how an otherwise boisterous crowd fell silent whenever he had the ball. They knew. Just before the hour, the Uruguayan won a free-kick in an innocuous position after being fouled by Elliot Ward. One moment Suárez was rubbing his head and claiming that the Bournemouth centre-back had elbowed him, the next he was sending Sturridge through to slide a confident finish under Lee Camp.
Conceding again knocked the stuffing out of Bournemouth and, as they tired, Suárez and Sturridge began to torment them. Yet further punishment would have been harsh on Bournemouth, who were warmly applauded at the final whistle. Liverpool were content with two anyway. Now for Everton.