Poor defending cost them a second goal just before the interval, to Sadio Mane, who added a third after 53 minutes from an offside position.
Replacing Salah in the dying minutes, Daniel Sturridge converted his first touch after coming on as a late substitute. A languid pre-season campaign coupled with four of their 10 new signings in the starting line-up only compounded matters for the Chilean. Just how Clyne feels about that is one to keep an eye on.
Trent Alexander-Arnold almost doubled the lead five minutes later but West Ham goalkeeper Lukasz Fabianski pushed his free kick away from the near post.
The Guinea worldwide is as quick-thinking as he is quick-footed and proved he can dictate the pace at will, as evidenced by Mohamed Salah's opener.
Salah's goal featured an important contribution from new signing Naby Keita, while Guinea's Keita was excellent throughout.
Forget Gerrard, Liverpool haven't had anyone on this level since the days of Xabi Alonso and Javier Mascherano.
After netting six times in nine pre-season appearances, Sturridge went into this afternoon in fine goalscoring form.
Okay, the Brazilian did not score an own goal before being sent off and did at least manage 62 minutes, but such was the impact of his first-half display that he may as well have spent much of it in the dressing-room. After bagging against Arsenal and Watford in the last two years, he continued to wreak havoc amongst London clubs with a goal either side of half-time.
Sooner rather than later, the answer often fizzles out to a resounding "no".
City have ticked most of their boxes as we approach the 10-year anniversary of their takeover but they haven't ticked that one.
"I knew he was an aggressive player but by taking the No 8 shirt which has been vacant since Steven Gerrard left Liverpool three years ago, Keita proved before a ball was even kicked that he does not shy away from a challenge, " said former Liverpool midfielder-turned-pundit, Jamie Redknapp.
The champions, attempting to become the first team since Manchester United in 2009 to retain the title, were too good for an Arsenal side playing under new Spanish manager Unai Emery.
Will things be better this season? N'Golo Kante, Paul Pogba, Dele Alli, Harry Kane, Raheem Sterling, Romelu Lukaku, Eden Hazard: it was only four weekends ago that all of these players participated in the final games in Russian Federation, but they're already back and doing what they do best. And did they need another centre-forward in case Firmino is out? Robertson then connected with an unmarked Salah, who finished the low cross at the far post.