Mauricio Pochettino's men dominated possession at Molineux but wasted chances in an incident-packed game littered with careless defensive errors by the visiting side.
Wolves appeared to be cantering to victory after goals from Mario Lemina and Matt Doherty but they were made to sweat when Christopher Nkunku pulled one back deep into stoppage time on his Premier League debut.
The defeat means Chelsea are stuck in 10th in the Premier League, with Wolves behind them only on goal difference. No side have lost more Premier League matches in 2023 than Chelsea's tally of 19, while only three sides have lost more across the big five European leagues during the calendar year.
Pochettino bemoaned his team's missed chances after a frustrating afternoon. "We feel very disappointed because I think we deserve much more," the Argentine told 'Sky Sports'. "This competition wounds you when you are not clinical enough.
"We created chances. That is why it is so disappointing. We conceded after a few corners and it was really difficult."
He added: "We were talking a lot at the beginning of the season. We are young in age. It is a young team. We have players playing for the first time in the league. They need to adapt. It is confidence and about quality."
There were chances at both ends early in the game. Nelson Samedo burst forward but could not find Matheus Cunha on the left before Armando Broja stumbled on the ball in the box at the other end when well placed.
Chelsea's Nicolas Jackson was also guilty of failing to make the most of some good openings. The visitors wasted a gilt-edged opportunity to take the lead shortly after the half-hour mark when Raheem Sterling caught Joao Gomes in possession 40 yards out and drove forward.
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