Fonte found the back of the net with four minutes left to cancel out Ludovic Ajorque's first-half opener and put Lille on 59 points from 27 games.
They lead second-placed Paris Saint-Germain, who hammered bottom club Dijon 4-0 on Saturday, by two points, while Lyon will move within a point if they beat Marseille at the Stade Velodrome later on Sunday.
Strasbourg are now 15th on 30 points.
Lille dominated early on but Strasbourg were more clinical and they went ahead nine minutes before the break when Ajorque volleyed home from Frederic Guilbert's cross for his 11th goal of the season.
Ajorque went close to doubling the visitors' advantage with a header two minutes later but Lille goalkeeper Mike Maignan denied him with a superb save.
Strasbourg coach Thierry Laurey left the bench towards the end of the first half with broadcaster Canal Plus reporting that he felt unwell.
Fonte eventually levelled with a header but Lille were not able to take all three points despite a late effort.