"I thought we played against really slick Chelsea team in the first half, we gave away a poxy goal, so I was thrilled to get in at half-time only a goal down", said Hammers boss David Moyes, whose side are now six points above the relegation zone.
Willian was inches away from doubling Chelsea's lead early in the second half after Hazard's clever back-heel gave the Brazilian space to shoot just wide.Morata has endured a hard first year with Chelsea and his fortunes weren't improving as he headed over from a corner before having another effort disallowed for offside.
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.
The Blues played admirably well, and the away side wouldn't have seized the valuable point if it wasn't for Joe Hart's brilliant display of saves, although the result stung a bit for the hosts.
Arsenal equalised 11 minutes later through Pierre-Emerick Aubameyang, playing a one-two with Welbeck.
But with just nine minutes left on the clock Welbeck grabbed the victor.
It has been a whirlwind few weeks for Rice which have seen him make his senior worldwide debut and play a starring role in Ireland u21's dramatic last-gasp win over Azerbaijan last month. And in a still-tight Premier League relegation battle, every point can be crucial.
Many feel Liverpool have their top-four place pretty much sealed at this stage in the season, the lack of reaction to the Reds dropping points against Everton on Saturday underlines this. Perhaps unsurprisingly, his team looked disjointed, especially early on.
Chelsea played a large part in their own downfall as Gary Cahill's wayward header allowed Marko Arnautovic to pull the ball back in the Mexican's path to slam past Thibaut Courtois.
After Aubameyang's equaliser - his sixth goal in seven Premier League appearances since joining from Borussia Dortmund in January - Long came close again.
Welbeck missed badly in front of an open goal but redeemed himself with the victor.
"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".
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Belgian rider Goolaerts dies, aged 23
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