But a glut of injuries and failure to win any of the last three games against fellow bottom half strugglers means the Hammers are now just three points above the drop zone.
West Ham welcome Watford to the London Stadium on Saturday fresh from their 4-1 thrashing of Chelsea last time out.
The game is huge for both clubs and could go some way to deciding their Premier League status.
But given the negativity surrounding West Ham both on and off the field at the moment amid the sacking of head of recruitment Tony Henry and planned protests against owners David Sullivan and David Gold, the match is fast becoming a must-win for Moyes' side.
There is some rare good news this week, though, with star man Marko Arnautovic set to return to face the Hornets while experienced new signing Patrice Evra could also be involved.
Meanwhile both Michail Antonio and Winston Reid could return to the starting line-up in a much stronger looking Hammers side.
Moyes looks set to make three changes to the side which lost 3-1 to Brighton last time out and will have his bench bolstered by the addition of former France international Evra who joined on a free transfer this week.
Winston Reid in for Declan Rice
Rice is definitely the future of West Ham but has been caught out for goals in the last two games and the Hammers need experience to get to safety as quickly as possible.
Michail Antonio in for Sam Byram
Byram has failed to convince in his time at West Ham and was shocking in the Brighton defeat. With Antonio fit again after a long spell on the sidelines he will come back into the side to offer more power and pace down the right hand side.
Marko Arnautovic in for Javier Hernandez
Hernandez has scored a couple of goals of late and looks more potent under Moyes. But Arnautovic is West Ham's talisman and will come straight back into the side to replace the Mexican, who was desperate to leave the club in January.