"Chich has come on, he's come back from the other side of the world last week for us, and he's been [injured] so I'm so glad that he's got fit for us and got that decisive goal", Hart said.
It was only West Ham's third touch inside the Chelsea's penalty area.
Key upsets were losing to West Ham and Crystal Palace away, along with drawing to West Ham at home on Sunday.
And Hammers boss Moyes agreed Rice was making himself hard to leave out of the current starting XI.
"It's something that happens, sometimes you get - I don't know, it's difficult to say that because I don't want to speak bad about them because that's part of football".
'The Little Pea' made a big impact with his equaliser at Stamford Bridge - the sixth time in his career he had come off the bench to score against Chelsea. After the situation against Burnley, the club and the team have done a brilliant job, and the supporters today were outstanding.
Exploiting the space behind Cheikhou Kouyate, Hazard fashioned a series of chances for the Blues to wrap things up before the break.
As his influence grew, Morata also came alive.
Wilkins died at the age of 61 after suffering a cardiac arrest. "We have added another point to try and stay away from relegation".
They were made to pay for those misses when Hernandez expertly stroked home from Arnautovic's pull back to draw the Hammers level with 17 minutes remaining.
On forwards potentially lacking confidence: "Morata scored two offside goals".
Took his goal brilliantly and defended with purpose and urgency, as well as instigating many an attack and using the ball smartly.
Terry would make most Premier League XIs of the past 20 years so the comparison for the 19-year-old defender is huge.
"We can create a lot of chances but we cannot take them". His impact was instant and probably expected by large parts of the Stamford Bridge crowd.
Javier Hernandez hit the late equaliser as Chelsea's top-four finish hopes suffered a potentially fatal blow.
Belgian attacker Eden Hazard got a chance to give his side the lead in the 3rd minute but his shot went off target as the visitors were gifted a goal kick from the lose attack.
Released by Chelsea at 14.
There was an emotional tribute before the game, and after eight minutes of play, to Ray Wilkins, the former Chelsea captain and assistant manager, who died in midweek.
Morata's assist for Azpilicueta was the seventh time the two have combined in the Premier League this season - no two players have combined for more goals this campaign.
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