Sporting raced into an early lead through Carlos Mane inside the opening 10 minutes, and when Nani doubled their lead they looked to be on course for an easy victory.
An own goal from Jefferson gave Maribor a glimmer of hope before half-time, but their recovery was delayed as the lights went out at the Estadio Jose Alvalade, meaning the second half was delayed by 45 minutes.
When the action finally did resume, Islam Slimani restored Sporting’s advantage after 65 minutes with a perfectly timed volley, and their winning margin would have been even greater but for Maribor goalkeeper Jasmin Handanovic, who made a string of fine saves.
Nani, who impressed throughout, went close to doubling his own tally in the closing minutes, while substitute Fredy Montero saw two long-range efforts fly wide.
It did not matter in the end, though, as Sporting held on to an important victory, keeping their last 16 hopes well and truly alive.
Victory sees Sporting move above Schalke, who were beaten 5-0 by Chelsea, with one game remaining, while Maribor’s exit from the competition was confirmed.