Rene Girard's side moved to within a point of Ligue 1 leaders Paris Saint-Germain after Nolan Roux's injury-time winner gave them a 1-0 victory over Marseille on Tuesday.
This marks the 11th top-flight game in succession that Lille have kept a clean sheet, with Nigeria international Enyeama fast closing in on Bordeaux keeper Gaetan Huard's record of 1176 minutes without conceding, set in the 1992-93 season.
Enyeama - who has now gone 1035 minutes unbeaten - requires shut-outs in Lille's next two Ligue 1 fixtures at Huard's old club and at home to Bastia to set the new benchmark, but insisted his impressive streak is entirely down to a collective effort.
"What can I say? I'm just enjoying the moment," the 31-year-old told beIN Sport.
"It's not just me though, it's the whole group. We stay strong like a team. We have the spirit and the strength.
"I don't know what is possible now. All I can say is that I have a great team around me and a great set of coaches."
Enyeama last conceded a Ligue 1 goal in Lille's 2-0 home defeat to Nice on September 15.
