Son double spurs hopes of trophy for Pochettino
West Ham United 1 Tottenham 3
Mauricio Pochettino might give the impression of a man who cares little for such trifling matters as the League Cup but, with distant hopes already significantly dented in Tottenham's two priority events, this might yet be the competition that defines their season.
It is certainly shaping up to represent the best chance of what would be the first trophy of Pochettino's career and the club's first silverware in what has been an otherwise positive decade.
Son Heung-min was the difference here, clinically scoring twice in the absence of Harry Kane to clinch Tottenham's quarter-final place and ensure what was actually a largely competitive and positive West Ham United performance went unrewarded.
The proximity to Monday's 1-0 defeat against Manchester City had guaranteed significant changes to Tottenham's starting team and, while Pochettino was naturally unwilling to take obvious risks, he was still in the fortunate position of being able to start Christian Eriksen and Dele Alli.
Both had only been substitutes against City following injury and, with Harry Winks and Victor Wanyama forming a midfield base behind them of presence and quality, Spurs hardly looked significantly weakened.
West Ham had more of a mixture between youth and experience and, having scored twice in the previous round's 8-0 win over Macclesfield, the threat of 20-year-old winger Grady Diangana was quickly obvious.
He soon broke into space down West Ham's right and crossed well for Javier Hernandez, who opted to square the ball back along the six-yard box when a shot would have been a better option.
Tottenham initially seemed off the pace but an added quality among their attacking midfield players was soon evident.
Angelo Ogbonna had missed two opportunities to clear and was punished when Alli released Son.
The South Korean had actually not scored for 20 Spurs games but, with Kane rested, again stepped up in the absence of the team's attacking talisman to wrong-foot Adrian.
The home side did then take the game to Tottenham with more urgency throughout the rest of the first half, but struggled to find a decisive pass.
Hernandez and Obiang combined to release Michail Antonio but, having cut in dangerously from the left, his shot was deflected narrowly wide of Paulo Gazzaniga's left-hand post.
Still, West Ham pushed for an equaliser. Diangana's free-kick was perfectly flighted to bypass a mass of players inside the penalty area but Hernandez was just unable to get sufficient control with his chest.
Masuaka's midfield passing again proved inaccurate in almost releasing Hernandez shortly before half-time but Tottenham were able to maintain their slender advantage.
Manuel Pellegrini was decisive at half-time, replacing Felipe Anderson with Robert Snodgrass and his team resumed on the front foot.
Antonio and Snodgrass soon also had sights of goal, only for another defensive error to prove costly.
Spurs had launched a counter-attack but Alli's attempted pass was misplaced until it somehow bounced off Masuaku and into the path of Son. He was again one-on-one with Adrian and, on what was his 150th club appearance, was again clinical in this time taking the ball around the goalkeeper.
Pellegrini again tried to change things with some bold substitutions.
Strikers Lucas Perez and Marko Arnautovic were brought on and Spurs did wobble.
Arnautovic's sheer presence was the main threat and his cross was soon brilliantly cleared by Foyth. Gazzaniga, on a rare outing in the Tottenham goal, also made a save.
West Ham's pressure, though, would eventually get its reward. Arnautovic provoked another fine defensive challenge by Foyth but, from the corner that followed, Snodgrass's deep cross was headed past Gazzaniga by Perez.
The whole London Stadium was briefly roused but another needless defensive error really would end West Ham's hopes.
Eriksen's cross was missed by Ogbonna to allow Fernando Llorente a rare Spurs goal.
The sight of a pitch invader just before the corner was taken could arguably have had a distracting impact. The impact of the goal was less debatable.
West Ham and their fans knew that they were beaten and, save for yet another pitch invader, the stadium was largely emptied several minutes before referee Stuart Attwell did signal the end. (© The Daily Telegraph, London)