Wilder’s men trailed 2-0 to Chelsea at the break, after two strikes from Tammy Abraham.
But Callum Robinson, who’d earlier missed a golden chance to reduce the arrears, made amends with his first Premier League goal less than a minute into the second half.
And United rescued a point when Robinson’s cross took a nick – off either Kurt Zouma or Blades sub Lys Mousset – and nestled in Kepa’s net.
Robinson later told The Star he would be claiming the goal and Wilder added: "We had to play well here, we can't give ourselves a mountain to climb, which we obviously did.
"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."
Meanwhile, Jake Wright yesterday joined Bolton Wanderers on loan until January.
The centre-half, who was a key member of the Blades squad which won League One, hasn’t played a first-team game since 2018 and was told he was free to find a new club in the summer, after the Blades won promotion to the top-flight.
Wright, 33, became Bolton’s fourth signing on deadline day yesterday after their takeover was confirmed last week. Keith Hill’s men are battling to avoid a second successive relegation after beginning the League One season with a 12-point penalty because of their financial issues at the time.