Sio put the visitors ahead with a powerful header in the 50th minute and set Cedric Bakambu up for the winning goal with two minutes left.
Lyon, who hit the woodwork three times and recorded only five attempts on target out of 22, needed a 68th-minute penalty by Bafetimbi Gomis to find the net.
Lyon have not won in their four last league games and slipped to the third spot with 53 points after Olympique Marseille leapfrogged them thanks to a 1-0 win at Nice in the day's early kick-off.
"We have not to ruin everything after our very good first half of the season. Let's go back to work and keep our spirits up," Lyon captain Maxime Gonalons told French channel Canal+.
Marseille have 54 points and trail PSG, who beat Montpellier 1-0 at home on Friday, by seven. Nice are sixth on 48.
In the day's other game, Salomon Kalou and Nolan Roux were on target to help Lille climb to fifth on 49 with a 2-1 victory at 18th-placed Brest. The 2011 champions are just one point behind fourth-placed Saint-Etienne.
Sochaux moved up to 17th after completing a perfect 2013 record against the league's top three having beaten PSG and Marseille since January.
Although Lyon dominated possession from the start, the visiting side could have taken an early lead but Sio headed a Sebastien Corchia cross on to the post.
The Ivory Coast front-man, who joined during the winter transfer window, did find the net five minutes into the second half.
STRUCK WOODWORK
The home team pushed hard for an equaliser and Alexandre Lacazette went close to levelling at 1-1 but his shoot from the right struck the woodwork, a minute before he was awarded the penalty converted by Gomis.
Lyon laid siege to their gallant visitors' area but the bad luck continued as a Lisandro Lopez header struck the woodwork and Sochaux took advantage of a rare attack to regain the lead.
Clement Grenier could have saved a point for Lyon in stoppage time but his 25-yard free-kick was parried on to the crossbar.
There were fewer chances for Marseille in Nice but the first proved enough for Andre-Pierre Gignac to score his 10th goal of the season and earn his side their eighth away win.
Gignac headed home a Mathieu Valbuena corner in the 15th minute and wasted two other first-half opportunities to secure the victory for Marseille, who controlled the game thanks to their tough defence and collective discipline.
"We have been criticised but we have shown the same quality since the season started," OM coach Elie Baup told French channel beIN Sport.
"There are still eight games left and we will have to fight hard to stay on the podium."
It was not all good news for Marseille, however, as key centre back Nicolas Nkoulou had to leave the pitch in the second half with a thigh injury.
"I'll undergo some tests tomorrow," the Cameroon defender said.
