Ricky van Wolfswinkel put the Portuguese ahead in the 21st minute although the visitors responded as Miroslav Klose equalised five minutes before the break.
Emiliano Insua put the hosts back in front on the stroke of half-time with a 35-yard bullet strike.
However, the former Liverpool defender's night was ended shortly after as he was handed his marching orders early in the second half for a second bookable offence.
Sporting survived against a determined Lazio to clinch three points at the Jose Alvalade stadium.
Lazio, looking for their first win after their disappointing 2-2 home draw against FC Valsui in their opening group fixture, were under pressure early on with Insua's long-range effort forcing goalkeeper Federico Marchetti into an early save.
The hosts went in front soon after.
Van Wolfswinkel got behind Diego Capel's cross and beautifully flicked the ball past Marchetti.
On the half-hour mark, Stijn Schaars' curled free-kick was parried to safety by Marchetti.
In the 40th minute, Klose pulled Lazio level.
Hernanes sent the ball inside the area and Klose got past his market and struck a right-footed strike from 12 yards that beat Sporting goalkeeper Rui Patricio.
The hosts pressed forward before the break and were rewarded.
Insua's 35-yard bullet strike towards the far post beat Marchetti.
Sporting suffered a blow five minutes after the re-start when Insua was shown his second yellow card after a late challenge on Alvaro Gonzalez.
Lazio pushed forward and should have equalised in the 72nd minute.
Rui Patricio kept out substitute Giuseppe Sculli's bullet strike but failed to hold on to the ball and Adboulay Konko pounced from close range but was denied by the crossbar.
The Italians missed another great chance with three minutes remaining.
Lazio captain Tommaso Rocchi got his head on substitute Djibril Cisse's cross and his effort from a great position went wide in what should have been his 100th goal for Lazio.
Sporting, who won 2-0 at FC Zurich in their group opener, held on to take a strong grip in the pool.