Edin Dzeko grabbed two and Yaya Toure also got on the scoresheet as City all but booked a trip to Wembley by piling on the misery for the Hammers and their under-fire manager Sam Allardyce.
Johnson had been on loan at Sheffield Wednesday until last week, but opted for a move to West Ham instead of extending his stay at Hillsborough.
City needed just 12 minutes to take the lead at the Etihad Stadium and the Londoners were simply swept aside in an embarrassingly one-sided match.
Allardyce, who was taunted by visiting fans late in the game, had prioritised the game to some extent by fielding a weakened side against Nottingham Forest in the FA Cup third round last weekend.
But that backfired as they were thrashed by six goals and despite eight changes, including the return of senior players such as Mark Noble, Joe Cole, Guy Demel and Mohamed Diame, it proved a similar story in the Manchester rain. It was also a particularly chastening debut for Johnson, who looked well off the pace.
Such was City’s dominance that even Edin Dzeko lost track of the score: “It’s not easy to win 5-0 at home against another Premier League team.
“We still have to play away and this 5-0 – or 6-0, in the end – will give us the confidence for the second leg.
“The first goal is always important, then maybe we can open them up because they were defending with eight, nine players always. The first goal was also spectacular from Alvaro.”
Manager Manuel Pellegrini was delighted to as good as clinch a place in next month’s final at Wembley.
“Today was an important result to play at Wembley,” he said. “In football it is never finished until the end but today we have one leg in the final. The most important thing was not to score the six goals, it is the way the team must play.”