A goal in either half from Charlie MacDonald gave the O’s a 2-0 lead going into the final 40 minutes, but substitute Brett Pitman’s stunning volley seemed to have set-up a nervy ending in east London.
That was until Kevin Lisbie came off the bench to restore Orient’s two-goal advantage with little over ten minutes left to play.
With Harry Arter starting a two-game suspension, Richard Hughes was named in the starting line-up, while Matt Tubbs made way for Marc Pugh.
Playing in a 4-1-4-1 formation, the Cherries enjoyed most of the early possession and Lewis Grabban went close to making contact with Josh McQuoid’s dangerous cross as the visitors started on the front foot.
Orient started to grow into the game and created chances for Dean Cox and David Mooney, but neither could force Shwan Jalal into making a save.
And their pressure paid off in the 26th minute when Mooney got behind the Cherries defence and squared for MacDonald who was left with a simple finish inside the six yard box.
Full-back Scott Cuthbert almost added a second moments later as he dispossessed Matt Ritchie and then dragged a shot wide from a narrow angle.
The Cherries switched to 4-4-2 midway through the half, with McQuoid supporting Grabban, and the move soon paid dividends as the Northern Irishman played in his strike partner, who saw his effort saved by Jamie Jones.
With half-time approaching, only the width of the goal-line and the crossbar stopped on loan defender Dan Seaborne opening his account for the club.
His header hit the woodwork before being hacked away on the line by Romain Vincelot, and Seaborne was one of a number of players who appealed for handball against the O’s midfielder, who saw their protests turned down by referee James Linington.
The final chance of the half then fell to Vincelot who connected well with a half-volley, but saw it fly narrowly over the bar as Orient took their lead into the interval.
And they extended the advantage when MacDonald capitalised on Eunan O’Kane’s mistimed header to go one-on-one with Jalal and score his second of the afternoon with a cool finish just three minutes into the second half.
With more than half an hour left to play, Howe sent on Pitman in place of Wes Fogden and the January signing was denied by a full-stretch save from Jones a few minutes after his introduction.
But he found the back of net in the 65th minute with a stunning volley from O’Kane’s deep cross. Pitman timed his strike to perfection after being picked out by the midfielder to pull the Cherries back into the game.
However, they were soon facing a two-goal deficit again when Lisbie squeezed a shot beyond Jalal from the edge of the area following Moses Odubajo’s pull back.
Ryan Fraser made another late substitute appearance with the Cherries searching for another route back into the game, but they couldn't produce another goal for the strong travelling support to cheer.
Cherries: Jalal, Francis, Cook, Seaborne, Ritchie, McQuoid, O’Kane, Hughes, Fogden (Pitman 54), Pugh (Fraser 84), Grabban (Tubbs 73).
Unused substitutes: Allsop, Partington, MacDonald, Fletcher.
Goal: Pitman (65)
Leyton Orient: Jones, Cuthbert, Clarke, Baudry, McSweeney, Cox, James (Griffith 77), Vincelot, Odubajo, Mooney (Lisbie 69), MacDonald (Obafemi 89).
Unused substitutes: Grainger, Smith, Rowlands, Omozui.
Booked: Vincelot, Cox
Goals: MacDonald (26, 48), Lisbie (78)
Attendance: 5,136 (1,407 Cherries supporters)