Two deadly second-half strikes in the space of eight minutes from Warren Cummings and James Hayter saw Bournemouth safely through to the second round of the Carling Cup.
Leyton Orient dominated the opening stages and deservedly went ahead through Lee Steele after 12 minutes - but then paid the price for wasting a series of golden chances.
Bournemouth levelled on 33 minutes when Marcus Browning scored with a spectacular strike and from then on it was plain sailing for the visitors.
The defeat leaves Leyton Orient looking for their first home win since February but in the early stages they looked capable of pulling off a cup shock.
The League Two side took the lead with a splendid move when Lee Steele headed home after excellent work form Jabo Ibehre and Andy Scott.
Scott then laid on a glorious chance for Wayne Carlisle but he failed to take advantage and then Matthew Lockwood went close with a snap-shot.
But Bournemouth caught the home side on the break on 33 minutes and after a quick-silver move Browning sent a 25-yard drive into the top corner past a startled Glen Morris in the home goal.
That seemed to knock the stuffing out of the O's and the ever-dangerous Hayter hit a post just before the break after Wade Elliott's pacy run down the right.
After the break the O's started with a flourish and Bournemouth keeper Neil Moss acrobatically tipped Alan White's volley over the bar.
But the visitors quickly took a vice-like grip on the match and on 64 minutes Cummings cashed in on White's blunder when he intercepted the defender's tame pass and coolly rounded Morris to score.
Eight minutes later Hayter fired home Elliott's corner after Orient failed to clear.
Ibehre went close to cutting the deficit but Bournemouth always looked dangerous on the break and Hayter almost added a fourth but was denied by an excellent stop from Morris five minutes from time.