Zola credits a desire to role up the sleeves for the change in fortunes, though he insists West Ham are not safe yet.
"I'm very confident we'll stay up, even before Everton two weeks ago I said we will stay up. I won't change my mind on that," he said.
"We need to work hard as a team. The last few games haven't been pretty but the workrate and desire has been top class and that's why we will get important points.
"The danger has not gone yet so we need to keep working hard.
"Absolutely everyone is pulling in the same direction - everyone really wants this club to stay up.
"The mood here has changed and that's the good thing about football, things can change very quickly.
"We have a new belief so that even though we have not won at Liverpool since 1963, we know that we are not beaten before we get there. We will fight until the end."