Chris Wilder’s side appeared to be on the brink of a second successive Premier League defeat after falling two goals behind during the first-half of a memorable encounter in west London.
But Robinson’s effort immediately after the interval changed the complexion of the game, with United stunning the six-time English champions by snatching a last-minute equaliser.
Despite officially being credited as a Kurt Zouma own goal, both Robinson and substitute Lys Mousset claimed the strike with television replays later appearing to show the visitors’ Frenchman got the final touch on the ball.
Robinson, who had earlier spurned an opportunity to pounce before Tammy Abraham completed his brace, joined United from Preston North End during the close season and admitted opening his top-flight account had released a maelstrom of emotions
“I’m really happy, it came at a key time in the game,” said Robinson. “After I missed the chance, it was good to put it away.
“It was one of the best feelings I’ve ever had on a football pitch, to get my first Premier League goal. I didn’t know what to do, I just punched the air. You dream about doing that as a kid.”
Robinson’s drive and determination, after being guilty of missing arguably the best opening of the first period, set the perfect example for his team-mates to follow during a fixture which revealed the best and the worst of Wilder’s team.
Twice, Abraham pounced following lapses in concentration at the back.
But they dusted themselves down and, after being challenged to take the game to the opposition, Robinson’s finish and then Mousset’s late intervention stunned the home crowd.
Speaking afterwards, Wilder insisted he hoped the result would convince his squad they can compete with the best in the division.
Robinson echoed that sentiment, outlining the psychological effect it could have on a club which, only three years ago, was competing in the third tier of English football.
“The chance was playing on my mind,” acknowledged Robinson. “But the lads believed in me, the gaffer believed in me and Knilly (assistant manager Alan Knill) believed in me.
“We stick together. The lads at the back made a mistake but they’ve been brilliant all season.
“I missed a chance. But we stick together as a group.
“That’s what we do here. Everyone is in it together. We need to believe in ourselves even more.
“If we do that, then I think we can do really well and against some really good teams.”
Wilder believes the battling draw at Stamford Bridge will give his side confidence and belief for the rest of the Premier League season.
“We had to play well here, we can’t give ourselves a mountain to climb, which we obviously did,” reasoned the Blades chief.
“To come roaring back as we did in the second half hopefully gives us an enormous amount of confidence and self-belief going forward.
“I don’t want us to stand off teams, we obviously understand the teams we are up against and the journey we have been on.
“Three years ago we were bottom of League One and now we are going toe-to-toe in the Premier League. It’s not a cup tie, we are here on merit.
“From a biased point of view, I believe we deserved something from our second-half performance.”
Abraham, who opened his Chelsea account with a double at Norwich last week, needed only 18 minutes to grab a first goal at Stamford Bridge which may have England boss Gareth Southgate thinking twice about leaving him out of his youthful squad for the Euro 2020 qualifiers. The 21-year-old fired home after Blades goalkeeper Dean Henderson had fumbled his original weak header.
Whatever United go on to achieve this season, they will be remembered for their introduction to the Premier League of overlapping centre-backs and it was that approach that should have earned them an equaliser.
Chris Basham, who had earlier squandered a good chance of his own from the edge of the area, hooked a delightful ball across goal that was begging to be converted – but somehow Robinson squirmed his header wide from inside the six-yard box.
Just minutes later, Abraham doubled the lead.
Blades centre-backs John Egan and Jack O’Connell went for the same ball, allowing Abraham to nip in and fire home despite Henderson getting a hand to his effort.
Robinson then made amends less than a minute after the restart.
Enda Stevens got in down the left and cut back for the former Preston striker to fire home his first goal for the club.
Abraham remained a threat and would have been celebrating a hat-trick had it not been for Henderson, who brilliantly got down low to to keep out his England Under-21 team-mate’s shot from Cesar Azpilicueta’s cross.
The Blades continued to test Chelsea and put them under long periods of pressure and it was rewarded with the late equaliser.
Robinson impressively delivered from the left and Mousset got to the ball first to claim the final touch despite Zouma’s initial unwanted credit on the scoresheet.