Tuchel had only taken charge of one training session ahead the game following his appointment as Frank Lampard's successor on Wednesday, and although Chelsea saw far more of the ball, it lacked cutting edge and slumped to a disappointing draw.
Frustratingly for the host, its two best chances fell to full-back Ben Chilwell in either half, and otherwise there were few instances of Chelsea carving open the Wolves defence.
Nuno Espirito Santo's men went on to go closest to a winner when Pedro Neto hit the crossbar in the latter stages, leaving the Blues perhaps fortunate to hold on to a point.
Chelsea showed good intent at the start and should have had a fifth-minute lead when Callum Hudson-Odoi beat Rayan Ait-Nouri and delivered a teasing cross, but Olivier Giroud failed to get a touch on the ball.
That was not the start of a Chelsea onslaught, though, as they had to wait another 26 minutes for their next notable opportunity – Chilwell volleying off target from another good Hudson-Odoi centre.
Rui Patricio was eventually tested just before the half-time, the Wolves goalkeeper keeping Antonio Rudiger's header out of the bottom-right corner as Chelsea struggled to make the breakthrough despite completing more first-half passes (433) than in any other Premier League game since 2003-04.
The hosts' sharpest move led to their best chance just past the hour but again Chilwell could not capitalise, the left-back blasting over after Mateo Kovacic fed Kai Havertz and the German cut the ball back into the danger zone.
Neto was then presented with a wonderful chance to steal an unlikely win 19 minutes from time when he was played through after linking up with Daniel Podence, but his scooped effort over Edouard Mendy was kept out by the bar.
Chelsea piled the pressure on towards the end, with Kovacic going close from distance and Hudson-Odoi drawing a save from Patricio, but a winning start ultimately eluded Tuchel.