Thomas Tuchel's Chelsea reign got off to a frustrating start as Wolves secured a point in a drab stalemate at Stamford Bridge.
But the German was given an indication of the huge challenge facing him as his new team struggled to carve out chances against a Wolves side short of confidence and without a top-flight win since 15 December.
Rui Patricio produced good saves to keep out Antonio Rudiger's header and Callum Hudson-Odoi's deflected attempt, while Chelsea's 433 successful passes were the most by a Tuchel team in the first half of a top-flight game since May 2016.
Ben Chilwell sent a rare chance over the bar but Wolves, who hit the bar through Pedro Neto and gave a debut to striker Willian Jose, were good value for their point.
Meanwhile Chris Wood headed in a late winner as Burnley came from behind twice to grab an unlikely victory against Aston Villa in a thrilling match at Turf Moor.
Villa had been 2-1 ahead with 14 minutes remaining before Dwight McNeil's low cross evaded everyone for an equaliser and the midfielder then crossed for Wood to score Burnley's third.
The visitors dominated the first half and had gone in front when Ollie Watkins flicked the ball into the net following Matt Targett's low cross from the left.
After a number of fine saves by Clarets goalkeeper Nick Pope, the hosts levelled through Ben Mee's header, only for Villa to regain the lead with Jack Grealish's half-volley.
But Burnley, who had only scored five times in their previous eight home Premier League matches this season, found two more goals to ease their relegation concerns.
They remain 15th in the table, but are 10 points ahead of 18th-placed Fulham, who play away at fellow strugglers Brighton on Wednesday.
Elsewhere Tottenham manager Jose Mourinho expects midfielder Dele Alli to remain at the club after the January transfer window.
The England international, 24, has been linked with a move away from the club, with former Spurs manager Mauricio Pochettino reportedly keen on taking him to Paris St-Germain.
Alli has started only one Premier League game this season.
"The transfer window is open and sometimes unexpected things can happen but I don't expect it," said Mourinho.
"I am saying that since the beginning of the transfer window I was not expecting anyone to leave.
"I was not expecting anyone to come. Until now 27th Jan, almost at the end… I don't believe anything will happen but it's open, still.
"Football is football."
The transfer window closes at 23:00 GMT on Monday, 1 February.