Kakuta converted the spot kick early on at Stade Bollert-Delelis after Timothee Kolodziejczak's trip on forward Ignatius Ganago inside the box.
Florian Sotoca made sure of all three points which send the northern outfit a place off top spot on goal difference in the final 10 minutes after Wahbi Khazri's red card just after the hour mark.
"We certainly could have or should have scored the second earlier, it's obvious but despite everything we got it," the hosts' coach Franck Haise said.
"These 13 points we didn't expect them but we didn't steal them. We can't stop, we will work even during the international window," he added ahead of the two-week domestic break.
Patrick Vieira's Nice – the only side to beat Lens this term – claimed three points for the first time since the opening day of the season, overcoming Nantes 2-1 on the Mediterannean coast.
Brazilian defender Dante and Dephren Thuram-Ulien, the son of France FIFA World Cup winner Lilian, scored for the hosts after Andrei Girotto was sent for an early shower after a third-minute tackle on Hassane Kamara.
Imran Louza cut the deficit 11 minutes into the second half with a penalty but Christian Gourcouff's men remain without a win since 30 August.
On Monday, league leader Rennes welcomes Reims and UEFA Champions League semi-finalist Lyon faces Andre Villas-Boas's Marseille.