Neither the Argentine Lanzini nor Austrian worldwide Arnautovic are out-and-out strikers but with Andy Carroll injured, Moyes paired them up-front and they played like they had been a partnership for years.
West Ham are yet to recover from the loss of Dimitri Payet, but the Swiss winger and playmaker could help replace the missing contributions of the French star given their similar skill set.
Lolley made amends in great style five minutes before the break, beating West Ham keeper Adrian with a fine curling left-foot shot to send the teams in level at the interval.
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West Ham secured their first victory of the season when the two clubs met at the Olympic Stadium last September, bagging a 2-0 win thanks to late goals from Pedro Obiang and Andre Ayew. And to put an exclamation point on a banner second half day, Arnautovic and Lanzini connected once again for the Argentine's brace just five minutes later in the 61st.
For Moyes it brought up a significant milestone in his own career, as only Sir Alex Ferguson, Arsene Wenger and Harry Redknapp are the only managers to pass the 200 win mark in the Premier League era.
We're not sure yet but if it is the latter - and that would be a real shame - we will need to go out to try to make a suitable signing this month because we will need someone who plays down that righthand side.
"I'm really pleased with Marko Arnautovic".
"Everybody knew how good he was when he was at Stoke City and that's why they paid a big fee for him".