David Moyes’ side looked to be cruising towards the last 16 after goals from South Africa midfielder Steven Pienaar and French defender Sylvain Distin put the hosts two goals ahead just after half-time.
But Distin was sent off with four minutes left for a mistimed tackle in the penalty area and Miguel Veloso converted the spot-kick to leave the tie on a knife-edge ahead of the return on February 25.
Despite beating Chelsea in their last match, Moyes still made two changes to the Everton team, as Pienaar came in for Russia winger Diniyar Bilyaletdinov, while Nigerian defender Joseph Yobo replaced John Heitinga.
Everton nearly took the lead in the 12th minute when Australia midfielder Tim Cahill sent Louis Saha racing through on goal. The French striker, who has 15 goals this season, had to react quickly to get his shot off and Sporting goalkeeper Rui Patricio was able to block.
Cahill was in the thick of the action again when he headed wide from Leighton Baines’s corner.
Sporting have been in poor form of late and, with the second leg at home still to come, they were largely content to sit back in the early stages.
Abel tried his luck with a long-range effort midway through the half but he couldn’t hit the target.
Pienaar was sent off at Liverpool in his last appearance but the South African made amends for that in the 35th minute.
Phil Neville released Cahill and he back-heeled cleverly into the path of Pienaar and he showed tremendous desire to get to the ball ahead of his marker to shoot into the roof of the net for his sixth goal of the season.
That setback sparked Sporting into life and Marat Izmailov picked out former Rangers midfielder Pedro Mendes, who tested Everton goalkeeper Tim Howard for the first time.
Izmailov went even closer in the 40th minute with a ferocious effort from a tight angle that cannoned into the woodwork.
While Sporting had more bite going forward now, they still looked shaky at the back and it was no surprise when Moyes’ side increased their lead four minutes into the second half.
Baines swung in a corner and Patricio made a hash of his attempted catch, giving Distin the opportunity to poke home from close-range, although the defender didn’t know much about it as the ball hit him and went in almost before he had time to take aim.
Cahill limped off in the closing stages with an injury, but Patricio still needed to make two fine stops to deny substitute Ayegbeni Yakubu and then Saha in the closing stages.
Just as Everton looked home and dry, Distin was sent off after a clumsy challenge on Liedson and Veloso stepped up to slot home the spot-kick to give Sporting a lifeline. (SW/MG/rex)