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The Hammers proved obdurate opponents and made life difficult for City, taking a 43rd minute lead through Angelo Ogbonna's header.
But Pep Guardiola's side regrouped after the break and dominated the second half.
Argentine defender Nicolas Otamendi levelled the scores before David Silva celebrated signing his new contract extension with the club by sealing victory with a fine 83rd minute finish from Kevin De Bruyne's fabulous assist.
It was City's 20th win in succession and the Club's 13th consecutive league win – equalling a Premier League record.
And Delph, who produced a man-of-the-match display after starting in midfield and then moving to left-back after the break, said he had every confidence that City's composure and belief would eventually break down the Hammers defence.
"It was difficult, teams seem to come here and get every man behind the ball, not interested in anything but parking the bus," said Fabian.
"It has happened a few times but we have players like David Silva in the team, so we knew if we kept going we'd get our chances.
"We knew we had to be patient, we came out flying in the second half, we tried to explain to the boys we still had time and then we started to relax a bit more and found those spaces."
City now have the opportunity to create Premier League history at Old Trafford next week by registering what would be a record 14th straight league win – but Delph said no-one at the club was getting carried away.
"It would be nice to break the record at Old Trafford. We want to win the derby but we are taking it each game at a time," Fabian added.
"We are not thinking about what has happened in the past or looking too far into the future."
Man City team news ahead of the West Ham game...