The Blues, who were being managed by the recently appointed Thomas Tuchel for the first time, dominated large portions of the game but failed to really cause Rui Patrico with too many problems.
In fact, it was Nuno Espirito Santo's side that had the best chance of the game when Pedro Neto hit the bar when slipped through one on one with 19 minutes remaining.
Story of the game
Chelsea made a bright start to the clash and inside five minutes Olivier Giroud was close to handing the Blues the lead, but he could not get a touch on to Callum Hudson Odoi's low cross across the face of goal.
The hosts continued to dominate the majority of possession and were on the front foot without being able to break down the visitor's defence with Hakim Ziyech seeing a curling effort from range fly straight into the arms of Patricio on the 20th-minute mark.
Just after the half an hour mark with either side really managing to get a shot off, Ben Chilwell had an opportunity to hit the target when a Hudson-Odoi deep cross found the full-back at the back post, but he sliced his volley wide of the mark.
Tuchel's side continued to maintain control of the game and got off their second shot on target six minutes before the break, but Antonio Rudiger's header from a Ziyech free-kick was held down low by Patricio.
A minute later the Wanderers had their best opening of the game when, on the counter-attack, Neto found Leander Dendoncker unmarked inside the area, but his header floated over Mendy's crossbar.
With Ki-Jana Hoever coming on as a half time substitute in the place of Rayan Aït-Nouri, Chelsea's dominance continued and they had a penalty claim when Kai Havertz went over under a challenge from Nelson Semedo, but the referee waved away the claims.
In the 61st minute the first opportunity of note of the half was created when Havertz cut the ball into the path of Chilwell, but his first-time effort was sliced off target.
Three minutes later, Giroud was found in a bit of space from close range, but he failed to get the ball out of his feet as eventually, his attempt dribbled into the arms of Patrico.
Then despite not creating much at all, Wolves should have broken the deadlock when Neto's chipped effort found the bar instead of the back of the net when the winger was played through on goal by Podence.
In the latter stages of the game, the Blues started to pile on the pressure and with eight minutes to go, Mateo Kovacic was inches away from grabbing the winner, but his first-time effort from the edge of the box flew narrowly wide of the right-hand post.
Four minutes later, Patricio made his first meaningful save when he tipped Hudson-Odoi's deflected effort from the left around the post.
Then with the last kick of the game, Havertz thought he had snatched away all three points for Chelsea when his header from a corner from the right looked to be heading for the back of the net, but it deflected off new signing Willian Jose and out of play to secure an important point for the Wanderers.
First league clean sheet in 12 as a platform to build on
Tonight's result marks the first time that Wolves have not conceded a goal in a single league game since their 2-0 victory over Crystal Palace back in October.
This clean sheet further marks the first time the club have achieved back to back clean sheets since June 2020.
Therefore these statistics added on with the fact that despite Chelsea dominating 79% of the possession, the visitors limited them to very little signs of goal meaning that going forward this clean sheet can be something to build on.
This can further be seen to be the case through how Jose made his debut for the club today after coming on as a replacement for the recently returned Podence.
At this stage, this can only be seen as a positive due to how if over the coming week's Wolves remain sturdy and solid at the back and if the Brazilian does start to hit the ground running, the Wanderers could begin to get back to the sort of form that everyone has associated them with over the last two seasons in the top-flight.
Tuchel needs to time to find best 11
The former Borussia Dortmund and Paris Saint Germain manager was only appointed as the new boss of Chelsea yesterday following the departure of Frank Lampard, meaning that he has only been able to oversee one training session.
Consequently, this would explain some of the decisions that the German made in his team selection as he left out Mason Mount who had started in each of the last 13 league games.
He also chose to not select, Christian Pulisic, Timo Werner, Tammy Abraham (who claimed himself a hat trick last time out against Luton Town) and Kurt Zouma who was replaced by Rudiger.
At the start of the game, these could be considered to be slight surprise decisions especially in terms of creativity and with the hosts having created very little, it could be seen to be a decision that in the end were costly.
This is further proven by the fact that when Mount and Pulisic were brought on in the late stages of the game, Chelsea looked more dangerous going forward and this can largely be put down to both of their presences on the pitch.
However, with Tuchel having not had long to prepare his team ahead of this clash, blame can not be put down to him for this.
But over the coming days leading up to their next game against Burnley on Sunday, he needs to get the group together and start to create a system that accommodates and includes all of Chelsea's best players in order for them to still have a chance of finishing in the top four.
Stand out player- Max Kilman
The 23-year-old, who started his first league game since the end of December was very impressive in the back three along with the other two centre-halves beside him in the forms of Conor Coady and Willy Boly.
There were not many occasions at all in which a Chelsea forward was slipped in behind the defender and when being run at, he tended to stand firm as he was not beat in many dangerous areas.
Also when the hosts did pile on the pressure, he won most aerial duels that came his way and he was brave when committing into tackles in deep areas and when being forced to go into a block.