Jose Mourinho's side were living dangerously in the second half but eventually picked up a battling victory which sends them three points clear at the top of group G
Matic, who spent three years in Lisbon with Sporting's great rivals, Benfica, before returning to the Blues in January, converted Cesc Fabregas's cross after 34 minutes.
The Serb found the net in a half dominated by the visitors but the home side proved more competitive after the break to leave the result in doubt up until the final whistle.
The result sees Chelsea bounce back from their draw with Schalke at Stamford Bridge on matchday 1, while Sporting, who had previously lost just one of nine home fixtures against English opposition, will rue the end of an unbeaten run at the Estadio Jose Alvalade that stretched to 16 matches in European competition.
Having previously claimed that in-form frontman Diego Costa was incapable of playing multiple matches in a week, Jose Mourinho named the Spain international in his starting XI for the second time in four days, while captain John Terry made his 100th Champions League outing.
Costa was in the thick of the action early on - failing to slip a shot past advancing Sporting goalkeeper Rui Patricio after being sent clean through in the second minute.
It was the visitors who were dictating the early pace but Thibaut Courtois had to be on guard to scoop up a low Jonathan Silva cross from the left when Sporting looked to threaten the Chelsea goal for the first time.
Patricio got down well to deny Andre Schurrle as the Germany forward tried to round the goalkeeper after getting on the end of an Oscar through-ball in the 15th minute before Islam Slimani's downward header at the other end was comfortably held by Courtois.
Schurrle should have done better than skew wide of the left-hand post when Eden Hazard found him with a cut back in the 22nd minute but Matic finally made the breakthrough 12 minutes later. The 26-year-old midfielder peeled off at the back post to meet a Cesc Fabregas free from the left, sending a looping header over a helpless Patricio and into the back of the net.
A push by Filipe Luis on Nani on the edge of the Chelsea box drew the ire of all in green and white five minutes into the second half before Oscar squandered a one-on-one opportunity similar to Costa's early chance.
Sporting certainly looked more alert at the start of the second half - Nani sent an effort into the side netting, while Adrian Silva swerved a volley over the crossbar.
Filipe Luis and Mohamed Salah went close for Chelsea in the closing stages, while a curling strike from Nani whistled narrowly wide, and Mourinho may be concerned by his side's failure to put the match to bed.
However, news of a draw in Group G's other fixture between Schalke and Maribor, along with Costa's ability to last the full 90 minutes, should soon bring a smile back to the face of the Chelsea boss after picking up a valuable three points in his homeland.