The Uruguayan-born forward produced the stunning, swerving shot in the 75th minute to give Qatar their first home win in Group A of Asian qualifying to leave them on seven points from five matches in the fourth round stage.
They are level at the top of the group with South Korea and Iran, who were hosting Uzbekistan (five points) on Wednesday.
Lebanon are bottom of the group on four points from five matches with the top two guaranteed a place in the finals in Brazil.
Both Qatar and Lebanon are attempting to qualify for their first World Cup but for all the intent shown in Wednesday's match at the Al Sadd Stadium, both seemed short of the quality required.
That was until Soria scored with a shot worthy of winning the World Cup final after being given too much freedom to drive forward in a rare lapse by the otherwise assured visitors backline.
The goal relaxed the home side and they played out the final minutes with greater confidence. Substitute midfielder Lawrence Quaye close to capping a brilliant 20-pass move in the 85th minute but his rasping drive from 20 metres was parried behind for a corner by the Lebanon goalkeeper.
Lebanon, competing at this stage of qualifying for the first time after a fairytale run which has included victories over Asian heavyweights South Korea and Iran, had few chances in the match with a lack of quality in the final third letting them down.
But the visitors almost snatched a point when playmaker Roda Antar curled a shot towards the corner of the Qatar goal only for goalkeeper Qasem Burhan to produce a brilliant fingertip save to push it behind as the home side held on.
It was Qatar's second 1-0 win over Lebanon, who were ranked a lowly 146 by FIFA last year, in the campaign with Soria also grabbing the only goal when the two teams met in Beirut in June.
Next up for Qatar is a tough trip to South Korea in March with Lebanon also on the road in Uzbekistan.