Bonne’s 23rd minute strike from a David Mooney cross settled a close affair, earning the O’s a trip to League One outfit Gillingham.
The O’s made two changes to the side that drew at Dagenham & Redbridge on Saturday, Jamie Sendles-White was ruled out through illness while Alex Lawless was sidelined through suspension, Romauld Boco and Michael Clark replace them respectively.
Meanwhile academy graduate Charley Barker was named on the bench for the first time this season, meaning 10 of the 18-man squad had graduated through the O’s Academy system.
A slow opening ten minutes meant neither side created a clear enough chance to register a shot, however the first for Leyton Orient came from Myles Judd who headed Jake Caprice’s early cross wide of the target.
Dagenham’s first chance came after the O’s failed to clear a cross before the ball fell at the feet of Morgan Ferrier, who’s shot was deflected well behind the goal for a corner kick by Michael Clark.
The game lived up quickly as both sides searched for an opener, Macauley Bonne had a header saved by Cousins who then released Corey Whitely down the other end only to be denied by brilliant defending from Judd.
Minutes later however, Orient opened the scoring through Bonne who converted David Mooney’s cross with a headed effort that left the keeper grounded as it entered the net.
The O’s enjoyed decent spells of possession late in the first half as they looked to add to their lead, and five minutes before the break, Caprice’s long range shot stung the hand of Cousins after the wing-back drove forward.
On the stroke of half-time Morgan Ferrier saw a close-range effort fly high over the target after the O’s lost the ball deep in their own half due to a misplaced back pass.
Both teams returned for the second-half with Dagenham the only side to make a change, Okenabirhie was introduced in the place of Adams.
Moments after being introduced Okenabirhie saw a chance zip just wide of the post after Ferrier cut the ball back to the edge of the box from the right wing.
Almost immediately up the other end of the pitch, Caprice almost caught out Cousins in the Dagenham goal with an early cross, but the ‘keeper recovered well to tip the ball over the bar.
As the hour mark approached Mooney went down after he beat Cousins to the ball but the referee was not convinced and booked the skipper for simulation.
Again, the O’s stepped up their search for a goal and Bonne swung in a deep cross for Boco, but the latter could only fire wide of the target.
Charlie Grainger excellently denied Craig Robsinson who fired an effort at goal from just inside the box after a quick Dagenham attack.
Okenabirhie had another chance when he whipped a low ball across the face of goal, but there was nobody from the Daggers able to touch it goal-wards.
It was end-to-end play when Bonne darted into the box before collecting the ball, he then squared it to Mooney who’s touch takes the ball out of his control and allowed Ling to recover.
Nine minutes remained when Mooney was set free by Bonne’s flick on but a brilliant tackle from Scott Doe denied the skipper a chance to shoot.
Grainger palmed a powerful shot behind goal from Ferrier after the attacker forced his way into the box.
With time running out the visitors continued to push forward, but Grainger first denied Ferrier with a brilliant stop before Michael Clark produced a stunning challenge in the 95th minute to deny Okenabirhie as he lined up a shot to secure the O’s place in the First Round of the FA Cup.
ORIENT: Grainger, Caprice, Clark, Happe, Widdowson, Judd, Clay, Boco (Westbrooke 90+6), Dayton (Ochieng 83), Mooney, Bonne
SUBS: Sargeant, Koroma, Dalby, Sotiriou, Barker
GOALS: Bonne (23)
BOOKED: Mooney (57), Clark (77)
DAGENHAM & REDBRIDGE: Cousins, Doe, Robson, Adams (Okenabirhie 45), Ferrier, Romain (Cheek 65), Boucaud (Bloomfield 80), Lokko, Ling, Whitely, Howells
SUBS: Chapman, Nunn, Robinson, N’Gala
BOOKED: Robson (62)
REFEREE: Alan Young
ATTENDANCE: 2,013 (480)