Gradel hit his fifth goal of the season in the 19th minute to set the Cherries on the way to a well-deserved victory.
Brett Pitman had already given Orient a warning in the 11th minute when his 25-yard right footed shot whistled just past the right-hand post.
The Orient defence did not heed the warning and Gradel beat left-back Charlie Daniels for pace out on the wing before running into the box and finishing coolly past Stuart Nelson.
Bournemouth doubled their advantage ten minutes after the break after a horrendous mix-up in the Orient defence.
Centre-half Tamika Mkandawire under-hit his back pass to Nelson and teenage striker Sam Vokes stole in to calmly lob the ball home from 25 yards.
Orient woke up at this point and Adam Boyd forced a good save from Gareth Stewart in the Bournemouth goal on the hour mark.
Daniels almost atoned for his mistake for the first goal a minute later when his cross-shot tested Stewart in the Bournemouth goal.
Centre-back Brian Saah dragged his side back into the game in the 73rd minute.
Bournemouth failed to clear a corner and Saah rifled home a right footed shot into the bottom right-hand corner from 15 yards.
Orient pressed for an equaliser but were caught out badly at the back a minute before the end.
Goalkeeper Nelson went up for a corner but when the ball was headed away he was left in no man's land at the wrong end of the pitch.
Substitute Jo Kuffour set off on a 50-yard run before squaring to fellow sub James Henry, who rolled the ball into the empty net for his side's second home victory in a row.