The draw pushed Chelsea up a place into fourth spot in the Premier League, level on points with third-placed Spurs and one point ahead of Arsenal, both of whom have a played a game less.
United are four points behind fourth-placed Arsenal, with a game in hand, as they search for a way into the top four and a place in next season's Champions League.
Harry Kane headed in a last-gasp equaliser to earn Tottenham Hotspur a barely-deserved 2-2 draw in a feisty Premier League derby at Chelsea that ended with both managers being shown red cards after the final whistle on Sunday.
Arsene Wenger cut a frustrated figure after his 10-man Arsenal side suffered a 2-0 home defeat to Bayern Munich in their Champions League Round of 16 first-leg clash at the Emirates Stadium on Wednesday.
Chelsea's 0-0 home draw with second-placed United ensured Thomas Tuchel is still undefeated in nine games since replacing Frank Lampard, but it meant they failed to dislodge fourth-placed West Ham United who became Manchester City's 20th successive victims in all competitions on Saturday.
However, one goal proved enough for City who picked up their sixth successive league win to move four points clear of Liverpool, who host Aston Villa later on Saturday, at the top of the standings.
Leaders Manchester City were held to a 0-0 draw at Crystal Palace
Timo Werner scored his first goal of the season as a much-changed Chelsea side crept into the fourth round of the League Cup by beating Aston Villa 4-3 on penalties after the Stamford Bridge clash ended 1-1 on Wednesday.
IMAGES from Europa League matches played on Thursday.
Arsenal extend Aubameyang stay with new three-year deal
Arsene Wenger would be an ideal England coach and the Football Association should be prepared to wait until his Arsenal contract runs out in order to appoint the Frenchman, former FA executive director David Davies has said.
With a squad that was derided for being short on quality by frustrated fans in pre-season, Arsenal, who host Norwich City on Saturday, have surprised many by surging to the top of the Premier League table.
Manchester City needed a second-half penalty from striker Erling Haaland to break the resistance of a dogged Crystal Palace.
The result moves Chelsea up to eighth in the Premier League table with 30 points, while Wolves are 13th with 23 points.
Champions Chelsea have not enjoyed the best of starts at home this season and face their biggest test yet on Saturday with the visit of free-scoring leaders Manchester City.
Arsenal are eighth, seven points adrift of fourth-placed Chelsea, while Norwich remain second from bottom.
City were given a stern test on a wet and windy night at a noisy Kassam Stadium but two goals from Raheem Sterling eventually saw them through.
Arsenal's Laurent Koscielny is the best defender in the Premier League, according to former England and Manchester United centre-back Rio Ferdinand. Ferdinand also praised the Gunners backline in Wednesday's impressive 3-0 Champions League win over Greek champions Olympiakos Piraeus, which sealed their progress to the knockout stages for a 16th consecutive year.
Images from the English Premier League matches played on Wednesday night.
News of all that's transpired on and off the football field
Guardiola has crafted a sleek offensive unit but, after a breathless opening 15 minutes at The Emirates, they appeared to ease off as their intensity levels dropped and they allowed Arsenal back into the match.
Images from EPL matches played on Saturday.
'When the war against Ukraine that Putin started is not going the way he was expecting it to and his military options are getting onerous, a bit of nuclear sabre rattling is what he hopes will turn things around for him and Russia.'
IMAGES from the English Premier League matches played on Saturday.
Arsenal manager Arsene Wenger has risked angering frustrated fans by saying the under-performing London club do not need any January signings if everyone in the current squad stays fit.
Barcelona's rampant trio of Neymar, Luis Suarez and Lionel Messi all found the net at the weekend and unsung Leicester City found themselves in the record books when their England striker Jamie Vardy scored for the 11th straight game.
Five talking-points from the Premier League weekend after Manchester United extended their winning run against Tottenham Hotspur, Liverpool were made to work hard for their win at Brighton & Hove Albion and Arsenal losing at West Ham United.
Danny Welbeck says he has emerged mentally stronger after a knee injury ruled him out of the 2016 European Championships and the 27-year-old is keen to make an impact in next month's World Cup in Russia.
Dutch soccer star Robin van Persie returned to his home ground on Monday as he signed with Feyenoord Rotterdam hoping for a positive ending to his dwindling career.
Images from the English Premier League matches played on Sunday night
Manchester City manager Roberto Mancini used every attacking weapon at his disposal on Saturday and was left frustrated after the various combinations failed to get the better of Everton.
Sweden's stunned players blamed poor luck for their 3-2 defeat by England in a thrilling Euro 2012 Group D match at the Olympic Stadium and thought they were the better team on the night.
Arsenal striker Park Chu-young has been left out of the South Korean squad for next month's final round of 2014 World Cup qualifiers amid a backlash from fans over his controversial decision to delay his mandatory military service.
Bayern Munich eased past title rivals Borussia Dortmund 3-1 on Saturday to secure their 10th consecutive Bundesliga crown in front of a sold-out home crowd and with three games to spare, while Paris St Germain secured a record-equalling 10th French top flight title after stuttering to a 1-1 home draw by 10-man RC Lens.
Pierre-Emerick Aubameyang scored his first three goals for Barcelona in a 4-1 win at Valencia, but Inter Milan suffered a shock 2-0 home defeat by Sassuolo. Images from the football matches played on Sunday.
News of all that's transpired on and off the football field
A round-up of Wednesday's action in the UEFA Champions League.
Manchester City had to battle back from behind to earn a 1-1 draw against Premier League newcomers Wolverhampton Wanderers who gave the champions a real test at Molineux on Saturday.
Marcus Rashford scored twice as Manchester United extended their 100 percent record on the road, coming from behind again to win 3-2 at the English Premier League's bottom club Sheffield United on Thursday.
A round-up of Tuesday's action in the UEFA Champions League.
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