But some aspects of West Ham's performance left fans disappointed. One was Andy Carroll's display, with the target man struggling for the second week in a row.
Another, however, was Zarate's performance after coming on as a second-half substitute.
To his credit, the 28-year-old took to Twitter to apologise for his cameo - an admirable step not taken by many other professional footballers. And that apology attracted plenty of praise and forgiveness from West Ham fans. Some were still left frustrated by the Argentine, though, and accused of him of producing a 'selfish' display against Everton by never passing or finding the right cross.
Here's how West Ham fans reacted on Twitter to Zarate's display v Everton. He has plenty of backing from supporters - but some aren't best pleased!
Zarate is the worlds most frustrating player, angers me so much. Got to admit though John Stones is a class player. #whufc— Jack Davies 父 (@JackEDavies) November 7, 2015
Does Zarate know how to pass or cross? Angers me so much. #whufc— Let's Get Hammered (@GetHammeredFP) November 7, 2015
And people moaned at me when I said Zarate was a selfish player. He needs to learn when to pass. #WHUFC— Scott Burgess #27 (@Scott_Burgess) November 7, 2015
@mau_zeta Thanks for having he balls to admit it. Try not to be so greedy and put a couple of balls in for your teammates.— Jarrod J Steel (@BecontreeHammer) November 7, 2015