The Brazilian scored 45 seconds after coming on to the field, playing a neat one-two with Eden Hazard before calmly slotting beyond goalkeeper Tomas Vaclik.
Chelsea started promisingly at the Generali Arena, with Frank Lampard's early shot held at the second attempt by Sparta goalkeeper Tomas Vaclik.
Hazard twice tried to engineer an opening for Fernando Torres, but on each occasion the World Cup winner did not contest good crosses into the six-yard box.
Sparta debutant David Lafata was causing Chelsea problems but the visitors continued to create chances at the other end, Torres heading over a Juan Mata free-kick from Juan Mata in the second half and Lampard heading straight at Vaclik.
Torres' evening was summed up when he shot right-footed from 20 yards, the ball slicing high and going out for a throw-in.
Mata made way after 82 minutes for Oscar, who made an immediate impact, receiving a return pass from Hazard before clinically finishing into the bottom corner.
The result, following last Saturday's 4-1 Premier League defeat of Wigan, saw Chelsea claim back-to-back wins for the first time since December and keep a clean sheet for a second time in eight games.