Having scored twice in the first leg, Sakho had a night to forget in Andorra, although his 14th-minute sending off made little difference - however he will now miss the second-round qualifying clash with Maltese side Birkirkara.
Elliot Lee's first ever goal for the Hammers was enough to secure his side's progression.
Slaven Bilic had been criticised by Lusitans coach Xavi Roura for disrespecting his side by not being involved in the opening leg - but the new West Ham boss was on the touchline to see his side go through with ease.
With the majority of his first-team squad returning to London after a pre-season training camp in Dublin, it was another side balanced with youth and experience.
James Tomkins again captained the side with Joey O'Brien making his 100th appearance for the club - as Matt Jarvis and Morgan Amalfitano also started.
The night got off to a bad start, with last season's top goalscorer dismissed after an incident off the ball that saw the Lusitans players surround referee Anders Poulsen - who obliged their calls for Sakho to be sent off.
Despite the early setback, the visitor was in front seven minutes later as Sakho's strike partner Lee opened his Hammers account.
The 20 year-old coolly converted Matt Jarvis's flick to grab the only goal of the night - although he threatened a second moments later but was knocked off the ball as he ran through on goal.
Lusitans winger Jose Aguilar had been niggling away at West Ham's players for much of the game having made an enemy of himself in the opening leg at Upton Park.
He came close with a 35-yard free-kick in the second half before defender Moises San Nicolas headed home - only to see his effort chalked out for offside.
There were late chances for both sides as Lee came close to adding a second late on but his curling effort bent the wrong side of Gerardo Rubio's post ,before Tomkins was on hand to clear Alfi Conteh-Lacalle's injury-time free-kick off the line.
