The backdrop to the game was all about the untimely death in midweek of Ray Wilkins.
The point takes the Hammers six points clear of the relegation zone.
It was the least the home team deserved for their domination.
Six times in 2018 (in all competitions) Chelsea have nursed a one-goal lead, only to watch it evaporate.
Chelsea began to crank up the pressure shortly after, increasingly filtering their play through Hazard and Willian.
Andreas Christensen is handed a rest, amid a testing breakthrough campaign for him at Stamford Bridge, while Alvaro Morata once again leads the line.
39th minute PASS: Works hard to win the ball in his own half and flicks the ball over a couple of Southampton players to send Elneny away. The game ended as a draw. But we were always in with a chance at 1-0. A season of frustration boils over when the manager and players realise that they are in fact in the shop window, and there stock is fading in the sunlight.
"This game describes it very well our season".
On forwards potentially lacking confidence: "Morata scored two offside goals".
It was a fine intervention so to ship from Hazard's resultant corner, played short, felt horribly careless on the visitors' part. But I think West Ham will start well, and I'm going to back them to be ahead at half-time, at [7.0]. Just like that West Ham are level. "Chelsea can get a goal in other ways but from a corner was really bad from our point of view".
Javier Hernandez believes the club are moving in the right direction but has stressed the importance of retaining momentum after Sunday's result, with The Hammers unable to afford many slip-ups.
Moses had another chance on 69 minutes to get on the score sheet after cutting inside only to see his curler fly just past the post.
"We have to try to do everything to continue to have the possibility to fight for a place in the Champions League", he said. They beat Manchester United in 2001-02 and drew 2-2 at Chelsea in 2015-16. Chelsea lost at home to Tottenham for the first time in the Premier League era and therefore find themselves huge outsiders for a Champions League place, now eight points behind Mauricio Pochettino's side.