Eden Hazard was arguably the only one of Chelsea's four starting attacking players to emerge with any credit in attack - Oscar's defensive workrate earned him a pass mark - as Mourinho was again left to bemoan his side's lack of cutting edge.
The impressive Hazard gave Chelsea an interval lead, but Samuel Eto'o spurned chances to double the advantage either side of half-time. The best saw Eto'o denied by goalkeeper Gerhard Tremmel from point-blank range in the opening seconds of the second half as the Blues' lack of potency was again illustrated.
Mourinho has recently spoken of his unease every time his side miss a chance, knowing it could prove costly in defence. Swansea scarcely threatened, but as long as there was just one goal in it the Blues were vulnerable and Mourinho knew it.
The visitors could not find an opening, though, leaving them with one win in six as Chelsea claimed en eighth win from nine home games this season to extend Mourinho's unbeaten Premier League record at Stamford Bridge to 69 games.
6’ – CHANCE FOR THE SWANS: Amat heads over from Shelvey’s free-kick from the left.
17’ - CECH TO THE RESCUE: Great save by Cech to deny Routledge with a shot from a tight angle but the winger is flagged off-side.
19’ – WILLIAMS SAVES SWANSEA : Terry's header across goal is cleared off the line by Williams as Eto'o was waiting to pounce.
28’ – GOAL FOR CHELSEA: Hazard gives Chelsea the lead with a vicious effort that went under the keeper’s body, he should have saved it.
31’ – GLARING MISS: Alvaro’s effort over from 6 yards is easily tipped over by Cech, he should have scored.
41’ – BLUES GOES CLOSE: Eto'o's effort from six yards out is parried by Tremmel, great save.
45’ – ETO’O MISS: Chelsea get us underway and go close to making it 2-0 when Eto'o gets on the end of Mata's cross but shoots straight at the keeper from 5 yards out.
48’ – ETO’O AGAIN: It's just not Eto'o's day, another low shot trickles wide from the edge of the box.
86’ – CHANCE: Bony flicks a header wide, he was unmarked and should have done better.
Eden Hazard has scored nine goals this season.
Swansea are without a win in their past five matches.
Was Samuel Eto’o a bad buy? The Cameroon striker was one of the most deadly strikers at Barcelona. But he looked way past his best and missed a host of chances that would have put this game to bed.
MAN OF THE MATCH
Ashley Williams (Swansea City) - Williams produced a dominant display and was unlucky that he blocked the keeper’s vision for Hazard’s winning goal.
CHELSEA: Cech 6, Ivanovic 6, Luiz 6, Terry 6, Cole 6, Ramires 6, Mikel 5, Mata 7, Oscar 6, Hazard 8, Eto'o 5. Subs: Lampard 6, Schurrle 5, Willian 5.
SWANSEA: Tremmel 5, Rangel 6, Amat 6, Williams 9, Taylor 5, Britton 5, Canas 5, Shelvey 6, Pozuelo 5, Routledge 6, Vazquez 5. Subs: de Guzman 5, Hernandez 5, Bony 6.