And Evra, a man who transcends football, came on to chants of "I love this game" from West Ham supporters and delivered an energetic, disciplined display on the left hand side of defence.
Moyes' side weathered the early storm, however, and could have taken the lead themselves in the 14th minute when Marko Arnautovic pulled down a long ball in the penalty area.
The result helped West Ham create some breathing space in their quest for survival while Chelsea stuttered yet again and just three points separate them and Arsenal in sixth.
Javier Hernandez's ninth goal against the Blues cancelled out Cesar Azpilicueta's scruffy opener. It was his eighth goal of the season for West Ham, and second equalizer as a substitute.
The Hammers earned a vital point as Javier Hernández netted a late equaliser to secure an unexpected 1-1 draw, moving his side one step closer to safety.
But on Sunday, with the Hammers trailing 1-0 at Chelsea in the thick of a relegation battle, Chicharito came off the bench and did what he does best: Score goals - specifically in that supersub role, and specifically against the Blues.
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Vettel snatched an opportunistic win for Ferrari in Melbourne two weeks ago, despite Mercedes clearly having the faster auto . That put him just ahead of Mercedes team-mate Lewis Hamilton , who has a five-place grid penalty so is set to line up ninth.
From there, the game was stretched, with Chelsea's Marcos Alonso drawing a good stop from Joe Hart - one of several brilliant saves on the day from the England worldwide.
West Ham are next in action when they host Stoke City on April 16.
The 3-1 loss to Spurs on April Fool's Day made three points the only option, but they hadn't counted on Hart being in such inspired form.
"Some of our players had heavy legs but we still won the game when we were questioned, I really like the spirit in this team", said manager Arsene Wenger. This game describes our season very well. I think in the second half we can finish the game.
"The thing is we have to start playing good football and winning games, because if we don't do that we can not get in the top four".
Hart was not used in either of England's friendlies against Holland and Italy last month, with Jack Butland and then Jordan Pickford getting the nod, while Burnley's Nick Pope is also in the frame.