Steven Whittaker - who netted a superb goal against the same team en-route to the UEFA Cup final three years ago - was on the scoresheet again on Thursday night but it was not enough to claim victory at Ibrox.
The tie now hangs in the balance ahead of next week's second leg in Lisbon.
Kyle Lafferty was handed the role of lone striker as Rangers made three changes from their 6-0 win over Motherwell, with El-Hadji Diouf making his debut playing just behind Lafferty.
As well as Lafferty, Richard Foster and Maurice Edu were both added to the team, with Kyle Bartley dropping to the bench.
Injury doubt Steven Naismith was also named among the substitutes, while Nikica Jelavic was ineligible for the European clash.
Rangers carved out the first real chance of the game when Madjid Bougherra weaved his way past a couple of players before unleashing the shot, but his effort was weak and easily smothered by goalkeeper Rui Patricio.
At the other end, a poor clearance from Allan McGregor gifted possession to Sporting, but the goalkeeper was able to breathe a sigh of relief when Maniche's tame shot fell well wide of the target.
McGregor then comfortably gathered a curling free-kick from Cristiano after the visitors had the chance to pile on the pressure when David Weir conceded a foul 25 yards out.
Sporting squandered another decent chance when Helder Postiga's angled drive fizzed across the face of goal and past the upright.
The best chance so far fell to Rangers when Diouf released Whittaker down the right flank and he provided the cross for Lafferty only for the big striker to nod over.
Diouf then tried to pick out Lafferty in the box for the header, but the goalkeeper punched clear before Whittaker hooked the rebound over.
McGregor came to the rescue of Rangers just before the break when he blocked a point-blank effort from Yannick Djalo.
Rangers looked dangerous after the interval and could have been ahead within a minute of the restart.
Diouf provided the knockdown for Whittaker and his thunderous shot drew a decent save from Patricio.
Rangers continued to press for the opener and Lafferty saw his shot deflected past goal before Sasa Papac's effort from distance also fell across the goal and wide.
The breakthrough came after 66 minutes when Whittaker rose above everyone else in the box to meet Vladimir Weiss' corner and dispatch a powerful header into the back of the net.
Sporting could have levelled when former Rangers favourite Pedro Mendes tried his luck with a shot that was spilled by McGregor.
Postiga followed up and rifled into the side netting but he was offside anyway.
However, Sporting claimed what could be a crucial away goal with a minute to go when substitute Fernandez met a cross from the right and bulleted a header past McGregor.
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