The Premier League side ran riot in the opening 45 minutes on home soil, with Lloyd Kelly, Alex Scott, Luis Sinisterra, David Brooks and Dominic Solanke on the scoresheet at the Vitality Stadium.
Kelly made the breakthrough in the seventh minute of the contest, finding the top corner with a stunning finish after a deep free kick from Brooks had caused all sorts of issues inside the Swansea box.
Brooks had his second assist of the match in the 10th minute, with the attacker delivering a dangerous cross into the Swansea box, where Scott was on hand to fire into the back of the net.
Swansea just could not deal with the intensity from the hosts, and two became three in the 14th minute when Sinisterra collected a clever pass from Scott before firing into the corner with a low strike.
The away side's clearest chance of the first period fell to Kyle Naughton in the 30th minute, but the defender's strike came off the post, with Bournemouth given a let-off in an otherwise dominant first period.
Solanke just missed the target in the 34th minute, but the Bournemouth fans did not have to wait long for another chance, and this one was taken, as Brooks was released by Solanke before picking out the bottom corner with a clever finish to end the match as a contest.
Bournemouth were not finished in the first half, though, and it became 5-0 in the 44th minute courtesy of a goal from Solanke, who had the simplest of tasks when Sinisterra delivered a low cross, firing into the back of the net, with Swansea's defence absolutely nowhere to be seen.
The visitors actually had the final chance of the first period, but Bournemouth goalkeeper Mark Travers was on hand to make a smart save to deny Liam Cullen.
There was no way back for the visitors in terms of the contest, but their supporters would have been looking for something to cheer in the second period.
There was an improvement at the start of the second half, with Cullen again forcing Travers to make a stop in the 56th minute, and there were chants of "we've got the ball" from the Swansea fans during a spell of rare possession from the away side.
The match was like a training session as the final 15 minutes approached; Kieffer Moore had a chance to add a sixth for the hosts in the 75th minute, but his effort was deflected wide of the post.
Bournemouth goalkeeper Travers made a save to keep out an effort from Jamie Paterson in the 80th minute, with Swansea looking to cap what was an improved second-half performance with a goal, but it was not to be for the Championship side.
The hosts, who had late half-chances to add a sixth through Marcus Tavernier and Moore, will now switch their attention back to the Premier League, preparing to head to West Ham United next Thursday, while Swansea will continue their Championship campaign away to the leaders Leicester City on Tuesday.