For much of the first half, the east Londoners did look second best, with Chelsea seemingly more unsafe with every attack.
"This season we have struggled and this game describes our season".
Javier Hernandez punished Chelsea's wastefulness with 17 minutes remaining after Cesar Azpilicueta's first-half opener for Chelsea.
Walker thinks that Chelsea needed the fans to step up in much the same way they do in away games.
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. This draw left Antonio Conte's side 10 points off Tottenham with only six games still to play.
But, after passing up one glorious chance, Welbeck headed home the victor nine minutes from time.
Fellow Ireland U21 global Josh Cullen made his second Premier League appearance this season off the bench against Chelsea yesterday, his third in total.
I would have probably commented earlier in the season that Chelsea's last few games look like a cakewalk for the most part, but Chelsea haven't been winning the easy games. The Spaniard's performance forced West Ham to defend for most of the game. Instead we are talking about a draw.
"We could have done better, of course, we gave them a gift, it was the first clear chance they had and they scored".
"How many times have I said we didn't take the chances we created?"
But next Monday they host fellow strugglers Stoke knowing a defeat would drag them right back into trouble ahead of a tricky run-in including fixtures against Arsenal, Manchester United and Manchester City. We can work with a lot of confidence after three points at home and a pretty good point here at Stamford Bridge.
"At the time I thought there was a bit on the ball". Patrice Evra got here in and did an excellent job off the bench. West Ham had mustered two touches in the opposition box prior to Javier Hernandez's strike, but Gary Cahill - on his return to the Chelsea team in place of Andreas Christensen - failed to cover himself in glory.