The victory takes Chelsea top of the group on four points after Schalke 04 and MK Maribor drew 1-1 in Germany to leave them on two points apiece and Sporting bottom with one point.
The defeat for Sporting ended their 16 match unbeaten record at home in European competition.
The 51-year-old Mourinho endured a frustrating evening as his side dominated proceedings but wasted a hatful of chances before hanging on against a resurgent second half Sporting side who came close on several occasions to salvaging a point.
“Three points is three points. We lost two at home and now we have picked up three away from home,” said Mourinho.
“Chelsea are a young team who sometimes show a lack of efficiency in front of goal. Sporting lost but they have arguments that they can qualify.
“We didn’t kill the game off but we played very well, very compact and we had complete dominance in defence. Now it is time to rest and then we will think about Arsenal,” added Mourinho in reference to Sunday’s Premier League clash at Stamford Bridge.
Chelsea got the breakthrough their first half dominance deserved, and the only goal of the match from a set-piece on 34 minutes.
A far post cross from the left flank by Eden Hazard was met by a Serbia’s Nemanja Matic and his looping header drifted over the head of Sporting captain Rui Patricio and into the back of the net.
Chelsea captain John Terry who turned in a solid performance in the centre of defence and was making his 100th Champions League appearance said his side should have wrapped it up sooner.
“They’re a very good side and played well but we had so many chances to kill it off but luckily Matic got the goal and we got the win,” Terry told Sky TV.
“We lost our first group match last season and came back to qualify but we had to win tonight and we got it so we’re top of the group and in control again.
“I’m very proud to reach a hundred matches, not many players have done that and I’m feeling great at the moment.”
For Matic, it was his second career Champions League goal in a country he knows well having played for Sporting’s city rivals Benfica, for three seasons before rejoining Chelsea in 2013.
“We played very well in the first half and played our game but we didn’t take our chances,” said Matic who came in for some stick from the Sporting fans over his links to Benfica.
“Well Sporting is a big rival of Benfica so I expected it but I’m very happy to score. It doesn’t matter who gets the goals as long as the team wins,” added Matic.
Mourinho, who enjoyed an early spell in his career as an assistant coach to Bobby Robson at Sporting between 1992 and 1993, gradually lost his composed demeanour on the sidelines as the match grew into a nailbiting affair.
Diego Costa broke the offside trap as early as the second minute and was clean through on goal from 30 yards but his low shot was deflected behind by Patricio.
Sporting came out after the break with more venom and came closest to their first goal of the match on 55 minutes when former Manchester United winger Nani spurned a close range chance with just Chelsea ‘keeper Thibault Courtois to beat.
Algerian Islam Slimani also threatened with a header from point blank range but Courtois was again well positioned to make the save.
Egyptian international Mohamed Salah had a chance to put the result beyond doubt in injury time when Chelsea again breached the Sporting back four but the excellent Patricio blocked again in a man-of-the-match performance for the home side.
Chelsea’s next match is at home against Maribor while Sporting travel to Schalke on October 21.