Everton appeared to be coasting to a well-deserved two-goal victory to take a healthy advantage to Lisbon for the second leg on February 25, but the match had a sting in the tail.
Distin was adjudged to have brought down Sporting's Liedson in the 85th minute.
He was sent off and Miguel Veloso gave Tim Howard no chance from the ensuing penalty.
Earlier Distin had put Everton 2-0 up four minutes into the second half when the ball hit him from a corner and rolled into the net.
The goal followed a well-struck opener from Steven Pienaar, who side-footed home on the run into the roof of the net from 12 metres out after 35 minutes to put Everton ahead.
The atmosphere at Goodison Park was subdued during the early stages of the match, which kicked off at the unusual time of 5:45pm GMT, in the middle of the Liverpool rush hour.
UEFA rules dictate that Everton and Liverpool, who face Unirea Urziceni in the competition on Thursday when the rest of the first leg matches will also take place, cannot play at home at the same time, and nor can Europa League matches clash with Champions League games which were taking place later in the evening.
Sporting's late goal added to the gloomy atmosphere at Goodison following the news before kick-off that Belgian midfielder Marouane Fellaini would miss the rest of the season with an ankle injury.
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