Frank Haise's team leapfrogged French champions Lille into seventh place with 50 points from 32 games. They trail third-placed Stade Rennais by six points and fourth-placed Monaco by three.
The top three qualify for the Champions League and the fourth-placed team end up in the Europa League.
Lille, who reduced the arrears through Xeka, are eighth on 48 points. They have lost to Lens in both of their Ligue 1 encounters this season and were also eliminated by their neighbours in the French Cup.
It is Lens's first victory at Lille in 19 years.
Lens went ahead after just four minutes when Frankowski found the back of the net with a half volley from Jonathan Clauss's cross.
Lille reacted with Renato Sanches's shot hitting the post but it was the visitors who struck again in the 37th, Kalimuendo beating Leo Jardim with a left-footed effort that took a deflection off Jose Fonte's thigh.
Lille reduced the arrears on the stroke of halftime courtesy of a Xeka header and hit the post again through Edon Zhegrova at the hour but Lens held on for a deserved victory.
Riot police officers were deployed after the final whistle as some angry Lille supporters tried to invade the pitch.