The visitors opened the scoring at the Cardiff City Stadium when Dan Gosling found himself with time and space on the edge of the penalty area before firing the ball past goalkeeper Simon Moore.
As the first half reached the midway point, the Cherries made it 2-0 after a sweeping move was finished off by Charlie Daniels, who made no mistake when driving the ball home from an acute angle.
Shortly after the half-hour mark, Bournemouth netted their third before the break as Gosling recorded his second goal when converting the rebound after Moore had saved from Brett Pitman.
Cardiff were in disarray, and caretaker bosses Scott Young and Danny Gabbidon made two alterations before half time as frustration grew among the club's supporters.
Seven minutes after the restart, Cardiff thought that they had pulled a goal back through Federico Macheda, but he was adjudged to have been offside after heading into the net.
Defender Juan Cala had no problem beating the offside trap but his header from an Adam Le Fondre set piece missed the target as the game continued to slip away from the home side.
Bournemouth almost made it four in the closing stages as Harry Arter struck the crossbar, but Eddie Howe's team were happy to settle for an emphatic win as Cardiff's woes continued in the opening weeks of the season.