The build-up to the game was dominated by talk of a two-year ban from European football imposed on City by UEFA for breaching Financial Fair Play regulations.
When Kevin De Bruyne is over the ball, anything can happen 😤— NBC Sports Soccer (@NBCSportsSoccer) February 19, 2020
Rodri scores for City! ⚽️ pic.twitter.com/sjYLJWwGjm
But it was business as usual on the pitch for City as Rodri made a breakthrough in the first half with his first home goal for the club and Kevin De Bruyne added a second just after the hour.
That proved enough for Pep Guardiola's men, who bounced back from their 2-0 loss at Tottenham earlier this month to open up a four-point gap on third-place Leicester City.
The original game was called off 10 days ago due to Storm Ciara which, combined with the competition's inaugural mid-season break, meant a 17-day rest for City's players.
He assists, he scores, he does it all 🔥— NBC Sports Soccer (@NBCSportsSoccer) February 19, 2020
Kevin De Bruyne doubles City's lead! ⚽️ pic.twitter.com/ltPBeyiUPn
It did not take long for the hosts to get going, Gabriel Jesus spurning a glorious chance by taking one touch too many in front of goal and allowing Ryan Fredericks to get back.
The Brazil striker again delayed the shot too long from City's next big opening, but Rodri opened the scoring with a looping header at the near post after half an hour.
Guardiola's men toiled for large parts of the contest but had a second goal after 62 minutes through De Bruyne, who exchanged passes with Bernardo Silva and fired home.
David Silva limped off with a knock in the final five minutes, shortly after Lukasz Fabianski produced a good save to thwart Jesus, but City cruised over the line to return to winning ways on home soil.
What does it mean? City do their talking on the pitch
The threat of a two-year ban from the Champions League has led to talk of a string of City's first-team stars, as well as boss Guardiola, moving on at the end of the season.
Guardiola challenged his players to focus on each game as it comes and this was a welcome win, 17 days on from losing at Tottenham in their most recent outing.
De Bruyne delivers again
De Bruyne sent in a delightful corner for Rodri's opener and blasted in a second to make it a combined 151 goals and assists for the playmaker in Europe's top five leagues.
Since making his City debut in September 2015, only Barcelona superstar Lionel Messi (62) has assisted more goals in Europe's top five leagues than the 61 De Bruyne has managed.
Hesitant Jesus lets West Ham off
Guardiola started Aguero and Jesus together in the Premier League for just the 12th time and West Ham struggled to cope with the pair.
Both players should have got on the scoresheet, though, with Jesus guilty of missing three gilt-edged opportunities.
City will be looking to preserve their four-point lead on Leicester when they head to the King Power Stadium on Saturday, while West Ham have a daunting trip to league leaders Liverpool in five days' time.