Lille conceded their first goal in 1,062 minutes of action during the clash which has left former Bordeaux goalkeeper Gaetan Huard's all-time record of 1,176 still intact.
"It makes me happy to beat Lille because they're a seriously good side," Gillot told reporters.
"There's a special flavour to it because it means a record hasn't been broken and I promised my mate Gaetan Huard that we'd do everything to stop his record being beaten.
"The win's great because we hadn't beaten a big team this season and now we have. We're on a good run with three wins in a row but things move fast in football and one defeat would almost throw everything into question again."
Bordeaux travel to Maccabi Tel Aviv in the Europa League on Thursday.