The Slovenians held off the Portuguese club for most of the match until the visitors struck with 10 minutes from time, but the hosts had the last laugh with a stoppage-time effort
The 18-year-old Portugal-born forward and son of ex-Porto and Benfica attacking midfielder Zlatko Zahovic salvaged the Slovenians a point in dramatic circumstances at Stadion Ljudski vrt after Nani appeared to have given Sporting an opening Group G win.
Sporting had themselves not appeared in the group phase since 2008-09, although the Primeira Liga side looked far more settled from the start, with Andre Carrillo striking the crossbar in the 26th minute.
Maribor eventually came to life towards the end of the first period and Aleksander Rajcevic hit the post with a powerful header.
But it was in the final 10 minutes that the tempo was finally increased as on-loan Manchester United man Nani broke the deadlock, only for substitute Zahovic to arrive off the bench to level matters in the third minute of stoppage time.
Sporting coach Marco Silva had attempted to play down the favourites' tag in the build-up, although his side soon found their rhythm as they dominated possession during the early stages.
The first chance of the game fell to the hosts, though, as forward Agim Ibraimi raced past Mouhamadou Naby Sarr and forced Rui Patricio to parry a stinging effort around the post with nine minutes gone.
Sporting responded as an attacking force 10 minutes later when Jefferson's curling free-kick towards the near post from the right flank had Jasmin Handanovic scrambling across his goal.
Nani then skewed a shot just wide a few moments later.
The visitors should have taken the lead through Carrillo in the 26th minute. The Peruvian linked up excellently with Islam Slimani on the edge of the area following a darting run inside, but he first fired straight at Handanovic when one-on-one and then struck the crossbar after collecting the rebound.
Maribor grew into the game at the end of the first half and, after spurning a couple of half-chances, Rajcevic nodded Dare Vrsic's free kick delivery on to Rui Patricio's right-hand post.
Sporting started the second half with renewed focus and they almost broke the deadlock in the 47th minute when Slimani's header from a Nani cross was knocked wide by Handanovic.
At the other end, Marcos Tavares – Maribor's play-off hero against Celtic with the goal that sent them through – went close twice.
The Brazilian saw an initial effort drop just wide of the post following a deflection off Cedric and then, just after the hour mark, his 20-yard attempt narrowly missed the target.
Nani, meanwhile, drew Handanovic into a smart stop in the 64th minute. But the on-loan winger was not to be denied in the 80th minute, as he jinked onto his left foot after cutting in from the right flank and sent a low effort into the bottom-left corner from 20 yards.
Sporting almost added a second following a goalmouth scramble but Maribor escaped and responded in the best possible fashion, with teenager Zahovic - an 82nd-minute substitute - arriving in the right place at the right time to head his sixth goal of the season after Mauricio had missed his clearance.
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