PABLO Ibanez's first Albion goal set up a comfortable passage into the Carling Cup third round.
The Spain international headed a 29th-minute opener from impressive debutant Sam Mantom's centre and super-sub Chris Wood put the icing on the cake with a more-than-deserved stoppage-time strike.
Roberto Di Matteo named a completely different starting XI for the Brisbane Road encounter.
And his much-changed side did not let him down as they produced a professional display to dispose of their League One counterparts.
Boaz Myhill kept a clean sheet at the other end on his competitive Albion debut.
The Wales international was rarely called into action but made a superb eighth-minute save to prevent the hosts opening the scoring.
Eighteen-year-old Academy product Mantom was handed his senior debut while summer signing Nicky Shorey made his full Baggies bow.
The visitors did the early pressing and Giles Barnes fired the first shot of the game in the fifth minute when he picked up a loose ball 18 yards out and saw his left-foot strike comfortably smothered by Jamie Jones.
Three minutes later, Myhill ensured the scores remained level as he pulled off a superb one-handed save to deny Scott McGleish from 15 yards after the ball had broken clear from a challenge between Leon Barnett and Jonathan Tehoue.
Mantom was coming more and more into the action and, in the 16th minute, he saw his initial cross rebound back to him before blasting a left-footed strike into the side-netting from a difficult angle.
Luke Moore tried his luck from 25 yards in the 20th minute but saw his low effort fly straight at Jones.
The former Villa striker came closer seven minutes later as he skipped past two players before forcing Jones into a flying finger-tip save to his right.
Moore then turned supplier and after Elliot Omozusi beat Barnes to his cross in the six-yard box, the ball fell to Roman Bednar who blazed a left-footed shot well over from the edge of the box.
An Albion goal had been coming and it duly arrived on 29.
Mantom delivered a pinpoint free-kick from the left and Ibanez nodded it across Jones and inside the far post to open the scoring.
Two minutes later, Simon Cox latched onto Shorey's pass and controlled on his chest before drilling a 15-yard volley a whisker over the bar.
At the other end, Tehoue managed to beat Barnett in the air in the 36th minute and found Charlie Daniels, whose first-time volley lacked the pace to beat Myhill.
The first half drew to a close with Bednar twisting and turning McGleish on the edge of the area. The Czech hitman got a shot away that was palmed around the right-hand post by Jones.
Orient boss Russell Slade made a double change at the break, with Dean Cox and Matthew Spring coming on for Omozusi and Mike Cestor.
After an uneventual opening to the second half, Di Matteo made a double switch on the hour mark as Wood and Marek Cech came on for Bednar and Barnes respectively.
The hosts had improved since the restart but showed no cutting edge.
However, Albion did have an escape when Gianni Zuiverloon scuffed his 64th-minute clearance, allowing Tehoue to cross for McGleish who headed wide of the right-hand upright when he should at least have hit the target from 12 yards.
Three minutes later at the other end, a poor clearance from Zuiverloon's cross fell to Mantom and he drilled a left-volley straight into Jones' arms from 18 yards.
Albion should have been two goals up in the 69th minute as Wood nodded down Zuiverloon's diagonal ball, only for Cox to screw his 15-yard volley horribly wide.
Mantom planted a corner straight onto the head of Wood four minutes later - but the New Zeland international sent his effort sailing over the bar.
An Orient counter-attack saw substitute Alex Revell flick on Dean Cox's cross from the right and McGleish headed goalwards, where Myhill easily plucked the ball out of the air.
Sub Cech had to be replaced himself, by Gonzalo Jara, five minutes from time after picking up an injury.
But Di Matteo's men continued to boss the game in the closing stages.
And Wood completed the job in the first minute of stoppage time as he muscled his way past two Orient players and drilled the ball home through Jones' legs from a tight angle.
ORIENT (4-4-2): Jones; Omozusi (D Cox HT), Chorley, Forbes, Cestor (Spring HT); Smith, Chambers, Dawson, Daniels; McGleish, Tehoue (Revell 70). Subs not used: Butcher (gk), Brown, Jarvis, Porter.
ALBION (4-1-4-1): Myhill; Zuiverloon, Ibanez, Barnett, Shorey; S Reid; Barnes (Cech 60 (Jara 85)), S Cox, Mantom, Moore; Bednar (Wood 60). Subs not used: Carson (gk), Olsson, Dorrans, Odemwingie.
GOALS: ALBION - Ibanez (29), Wood (90+1).
REFEREE: D Whitestone (Northampton).
ATTENDANCE: 2,349 (626 Albion fans).
ALBION STARMAN: Sam Mantom.PIC: ORIENT'S GOAL BLO...Ibanez celebrates his 29th-minute header with team-mates