Marcos Alonso opened the scoring before a superb solo goal from Eden Hazard and a strike from Cesc Fabregas sealed victory for Antonio Conte's men.
The January signing got a goal and assist as Pep Guardiola's side put the Hammers to the sword, helping them keep pace with the top four.
Zinedine Zidane's men had to ride out the jeers of their home crowd, but notched a commanding win to take advantage of dropped points elsewhere.
The Germany international set up his side's opener before rounding off a sound display with their final goal in a simple victory over the Latics.
Danny Welbeck netted a brilliant brace on his first Arsenal start since May before Theo Walcott's hat-trick offered further cheer for suspended manager Arsene Wenger, who watched a rampant 5-0 thrashing of Southampton from the St Mary's stands.
Luis Enrique's side will come up against Atleti as the two sides look to book their place in the final of the competition.
Luis Enrique's side remain in the hunt for major silverware after doing enough on home soil to make their way into the last four of the Copa del Rey.
The defending cup holders were not unduly troubled by the Rossoneri - who were reduced to 10 men - after they sealed victory in the first half.