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.
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.
Coach Marco Silva welcomed Mauricio back to the hosts' starting line-up after he served a one-match ban against Schalke, while Maribor made two changes from the side that earned an impressive 1-1 draw with Chelsea last time out.
A fast start from the Primeira Liga outfit saw Nani create a great opening that Joao Mario wasted, but in the ninth minute they had the lead as Mane netted his first Champions League goal.
Jefferson made good ground down the left before whipping a low cross into the six-yard box, where Handanovic was unable to claim the ball and the young striker was left with a simple tap-in.
Chances continued to arrive for Sporting, with Adrien Silva and Cedric unable to convert from good positions - the latter seeing a low shot pushed away by Handanovic.
With 10 minutes of the first half remaining, Sporting doubled their lead as Nani jinked past three defenders and lashed the ball beyond Handanovic from 12 yards.
However, in the 42nd minute, Maribor halved the deficit thanks to an own goal from Jefferson - the defender diverting Ales Mejac's cross out of Rui Patricio's reach.
Floodlight failure during half-time saw a lengthy delay to the start of the second half, but when the players eventually returned it was Maribor who posed the early threat, Zeljko Filipovic particularly dangerous.
They were unable to find a way through, though, and five minutes after the hour mark Slimani restored Sporting's two-goal lead.
Nani stretched to head Joao Mario's cross back towards the Algeria international and he volleyed home from seven yards out.
Slimani nearly doubled his tally two minutes later when Nani played an enticing ball into the penalty area. The striker beat two defenders in the air but Handanovic did well to push his effort away.
The Slovenian goalkeeper seemed to be fighting a lone battle against wave after wave of Sporting attacks and the 36-year-old was on hand to save another effort from Joao Mario after 75 minutes.
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.
