The former England midfielder has never scored a treble in 17 years at the very top of the game, but his goals proved all the more important as Bournemouth climbed out of the bottom four following the win.
On-loan Portsmouth midfielder Marc Wilson gave the Cherries a dream start when he coolly finished inside the penalty area on ten minutes by virtually passing the ball beyond Orient keeper Glyn Garner.
Anderton maintained the impressive opening with his first of the game six minutes later courtesy of an equally spectacular goal.
The veteran midfielder spun on the corner of the penalty area and bent an unstoppable shot into the far corner to give Bournemouth boss Kevin Bond a dream start.
A flood of chances then fell for both teams as Jack Cork went close for Bournemouth only to be denied by Garner and livewire Orient striker Jabo Ibehre was denied at the other end by Neil Moss.
All that proved irrelevant though as the well-aged feet of Anderton put the game beyond reasonable doubt when he latched on to a loose ball after James Hayter had been denied.
Minutes later, Anderton grabbed his third by stabbing home at the far post to end a 542-game wait for his first ever hat-trick.
The rout was completed when Hayter latched on to a long ball and ran free from a paper-thin Orient defence to slot past Garner.
With five on the scoreboard for the first time since they humbled Doncaster two years ago, Bournemouth could have carried on and made Orient suffer even more, but both Shaun Cooper and Hayter saw efforts drift just wide.