A first half goal from Danny Welbeck – his first in the tournament since October 2009 gave Arsene Wenger’s men the victory.
Arsenal started with Theo Walcott as captain with Calum Chambers and Rob Holding the centre-half pairing with Mathieu Debuchy at right-back and Sead Kolasinac at left-back.
Francis Coquelin and Mohamed Elneny were the defensive midfield shield with Joe Willock looking to have a slightly withdrawn role behind the attacking trident of Danny Welbeck and Walcott, with Olivier Giroud up top.
With Wenger opting for a flat back four the formation was set up as 4-2-1-2-1.
The Frenchman picked a young and inexperienced bench but it was interesting to note the three youngsters Arsenal signed up earlier this month on extended contracts, Eddie Nketiah, Ben Sheaf and Matt Macey, were all on it. No wonder Wenger called them the future of the club.
West Ham for their part made five changes from the side that were well-marshalled defensively during the 0-0 stalemate at the former Olympic Stadium last Wednesday.
Having failed to penetrate the steely resolve of the Hammers backline on a cold night in East London last week, these two London rivals again clashed, this time for a semi-final berth in the only domestic trophy Wenger has yet to win.
Backed by around 7,000 travelling fans which at least gave a half empty stadium a semblance of an atmosphere, the opening half an hour was nothing more than a scrappy affair with nothing of note to distract fans from searching for last minute Christmas presents on their mobile phones rather than the match itself.
There could have been more inside the ground but Islington Council turned down a request from the club to offer tickets on general sale after safety concerns following the large numbers of Cologne fans that infiltrated home sections during the Europa League tie in North London in September.
With seven minutes to go until the break Kolasinac broke down the left with some power and pace. He looked up and, not unnaturally aimed towards an unmarked Walcott in the box.
Walcott, who is 28 had no-one near him yards from the centre-spot. He had time with the goal gaping. Unfortunately he headed wide.
It was an action that was symptomatic of his 12 years at Arsenal – because after more than a century of goals for the club many are still waiting for him to produce his full potential. With glaring misses such as this one believers will be waiting a long time yet.
Thankfully six minutes later, Arsenal went in front. This time a header – a well-aimed, powerful one – from Debuchy into the box saw Welbeck cause confusion through his presence and managed to slot the ball home from a matter of yards out to make it 1-0, a mere 180 seconds before the break.
The second half started in much the same vein, with Joe Hart lucky to escape with only a yellow after he came flying out with abandon to fell an onrushing Welbeck with 18 minutes remaining.
The free-kick referee Kevin Friend gave was deflected with the subsequent corner coming to nothing. But it was sad to think of the decline of a once very good English keeper – one so talented, during his season-long loan spell at Birmingham City he made workaday defenders such as Roger Johnson look like England candidates.
Now Hart will be lucky to be England’s number one come the summer, with some cruel souls on social media now suggesting Miranda hart would have more chance.
Something has gone badly wrong in his career to end up as West Ham’s second choice loan keeper. As 18-year-old Reiss Nelson came on for a hard-working Giroud you hoped five years down the line this talented lad would be proudly flowering rather than festering like Hart.
And when Ben Sheaf – who this correspondent saw make his debut in far-flung Belgrade in October - replaced an industrious Willock it was refreshing to see such irrepressible youth given its chance.
But, the retort should have been if a youngster isn’t promising what is he doing in an Arsenal shirt.
As the final whistle blew on a timid 1-0 victory, it was instructive one had such thoughts. Because in an entertaining, action-packed match you simply wouldn’t have the time.
As it was Wenger’s men moved into the last four of the League Cup raising hopes of a tilt at silverware. .