Liverpool thumped Fulham to close the gap on leaders Arsenal to two points, while Aston Villa ended their recent goal drought with victory over Cardiff City.
Managerless Crystal Palace picked up a point after holding high-flying Everton at Selhurst Park and Norwich City moved out of the relegation zone.
Mourinho narrowly avoided his first league defeat at Stamford Bridge after Eden Hazard tucked away a debatable late penalty to salvage a 2-2 draw against West Bromwich Albion.
Chelsea went ahead just before half-time when Boaz Myhill pushed out Hazard's curling shot and Samuel Eto'o prodded home as Liam Ridgewell dithered in the six-yard box.
Shane Long saw a header come back off the post for West Brom on 57 minutes, but four minutes later, the Republic of Ireland striker drew the visitors level.
Petr Cech produced a brilliant reaction save to push Garath McAuley's header into the air and, as the ball dropped, Long showed the greater desire to head home.
West Brom then took the lead on 68 minutes following a counter-attack which ended with Stephane Sessegnon's low shot from the edge of the area somehow going through Cech's hands.
Deep into stoppage-time, Ramires went down in the box under Steven Reid's challenge and Hazard coolly rolled the penalty home to preserve Mourinho's unbeaten home record, much to the fury of West Brom's players.
Luis Suarez and Steven Gerrard stole the show as Liverpool beat Fulham 4-0 at Anfield to increase the pressure on Cottagers manager Martin Jol.
Liverpool were in front midway through the first half when Steven Gerrard whipped in a free-kick from the right and Luis Suarez's glancing header deflected off Fernando Amorebieta to leave Maarten Stekelenburg wrong-footed.
Fulham were undone by another set-piece three minutes later when Gerrard curled in a corner from the right and Martin Skrtel powered a header past Stekelenburg.
It was 3-0 nine minutes before half-time when Jordan Henderson's superb pass sliced open the Fulham defence and Luis Suarez finished past Stekelenburg.
The visitors continued to contribute to their own downfall when Kieran Richardson was caught in possession by Gerrard on 54 minutes and the Liverpool captain slipped in Suarez to score his second of the game.
Southampton continued their impressive start to the season with a resounding 4-1 victory over Hull City at St Mary's.
Mauricio Pochettino's side took the lead on 16 minutes when Nathaniel Clyne's cross hung in the air and Rickie Lambert nodded the ball back across goal for Morgan Schneiderlin to head beyond Steve Harper.
Veteran Hull keeper Harper then came racing out of his goal on the half-hour mark to bring down Adam Lallana just inside the area and Lambert hammered home the resulting penalty.
Lallana, who was called into the England squad earlier in the week, then showed just why he had caught the watching Roy Hodgson's eye as he skipped past two players on the left of the box before cutting inside and curling a low shot past Harper.
Hull were gifted a goal back 10 minutes into the second half when Victor Wanyama failed to control Artur Boruc's roll-out and the ball broke for Yannick Sagbo to steer a precise shot from the edge of the area past the Southampton keeper.
The Saints scored a fourth goal two minutes from time when Clyne whipped in a cross from the right flank and substitute Steven Davis controlled the ball and finished sharply past Harper.
Gary Hooper and Leroy Fer scored their first Premier League goals as Norwich came from behind to beat West Ham United 3-1 at Carrow Road.
West Ham took the lead on 32 minutes through Kevin Nolan's persistence as the midfielder kept the ball in play before teeing up Ravel Morrison to sweep home.
Norwich levelled on 54 minutes when Hooper powered home a penalty after the striker had been tripped by Jussi Jaaskelainen following a handling error by the West Ham keeper.
Jonny Howson crashed a shot against the bar on 71 minutes and, within 60 seconds, his former Leeds team-mate Robert Snodgrass curled a free-kick over the wall to put Norwich in front.
In the final minute of stoppage-time, Norwich made certain of the points as Fer broke into the penalty area before guiding a left-foot shot beyond Jaaskelainen.
Leandro Bacuna and Libor Kozak scored their second goals for Aston Villa in a 2-0 home win over Cardiff which ended a run of four games without a goal for Paul Lambert's side.
In a game of few chances, Villa took the lead on 76 minutes when summer signing Bacuna curled a free-kick over the wall and inside the post as Cardiff keeper David Marshall could only watch on.
A second goal arrived six minutes from time when Aleksandar Tonev's cross was headed back across goal by substitute Matthew Lowton and Kozak rose well to head inside the post.
Crystal Palace avoided defeat for only the second time this season after a 0-0 draw at home with Everton.
Palace had been the better team for long periods and Jerome Thomas forced a superb save out of Tim Howard in the first half before Marouane Chamakh headed off target.
Thomas came close again in the second period before Everton defender Phil Jagielka saw a header bounce back off the crossbar.