City had crushed Portuguese league leaders Porto 6-1 on aggregate in the previous round, but they found Sporting -- 14 points off the pace in the Portuguese Liga -- a much more obdurate adversary at Jose Alvalade Stadium.
Brazilian centre-back Xandao claimed the game's only goal with a clever back-heel in the 51st minute to give Ricardo Sa Pinto's side a narrow advantage ahead of the second leg at the City of Manchester Stadium next week.
Victory extended Sporting's unbeaten European home record to 10 games, while City coach Roberto Mancini was left to rue an injury to captain Vincent Kompany that forced the Belgian centre-back to leave the fray early in the game.
Gael Clichy started in an unfamiliar role for City at right-back and the visitors were forced to re-jig their defence again in the eighth minute when Kompany was forced off by an apparent calf problem.
Sporting right-back Joao Pereira sought to take immediate advantage of any uncertainty in the opposing ranks but after bursting into the City box, he saw his shot parried by Joe Hart.
City had started brightly, however, and they saw Kolo Toure force Rui Patricio into a save with a downward header before Gareth Barry curled a shot fractionally wide of the left-hand post from the edge of the area.
Sporting's Chilean playmaker Matias Fernandez fired a 30-yard warning shot wide at the other end, but although City looked untroubled at the back, they struggled to get their attacking players on the ball in dangerous positions.
The hosts ended the first half on the front foot and they carried their momentum into the second period, breaking the deadlock after six minutes thanks to a fine piece of innovation from Xandao.
After Hart spilled Fernandez's free-kick, Xandao saw his follow-up effort blocked by the England goalkeeper but when the ball came back to him, the Brazilian neatly adjusted his feet before back-heeling the ball into the net.
In response, Sergio Aguero drew a near-post save from Rui Patricio and Aleksandar Kolarov saw an attempt from just outside the box bend narrowly wide of the right-hand post.
City were indebted to an agile stop from Hart that prevented Ricky van Wolfswinkel from doubling the hosts' advantage in the 63rd minute, while Bruno Pereirinha poked a volley wide from Diego Capel's left-wing cross moments later.
Kolarov found the top of the crossbar with an over-hit cross but still City were unable to find gaps in the home defence.
Mancini reacted by sending on Mario Balotelli from the bench and the Italian almost carved out an equaliser with an audacious 'rabona' cross that David Silva stabbed wide at the near post.
The substitute came within inches of a leveller himself with three minutes to play, but his looping header from Silva's corner came back off the crossbar.