A much-changed home side had no chance of qualifying prior to their final Group H game against the French side but showing impressive energy and desire they took the lead in the 22nd minute when Christopher Jullien headed in from a corner.
Jonathan Ikone levelled two minutes later as the Hoops recent frailties resurfaced but Callum McGregor soon restored the home side's lead from the spot.
Timothy Weah, who had a spell on loan at Celtic, equalised in the 71st minute but 21-year-old midfielder Turnbull, a bit-part player since joining Celtic from Motherwell in August and making his European debut for the Parkhead side, drove in a third with impressive assurance.
The goal gave Neil Lennon's side their first win in six and will give the Hoops boss some respite from the flak he has taken during this recent poor run of form.
Lennon had promised to use his squad and made six changes with 22-year-old Northern Irish goalkeeper Conor Hazard making his debut and Ivorian midfielder Ismaila Soro given a first start with Turnbull, Patryk Klimala, Shane Duffy and Mohamed Elyounoussi back in the team.
Lille, who came from two goals down against Celtic to draw 2-2 in the Hoops' only fruitful group fixture in France, went into the game one point ahead of AC Milan at the top of the section and already qualified for the knockout stages.
However, the visitors were hoping to guarantee top spot to ensure a potentially more favourable draw.
The game took time to come to life in the driving rain but then came three goals in six minutes, starting when Celtic's French centre-back Jullien rose highest in the penalty area to head in a Turnbull corner from the left.
That lead lasted just two minutes before Lille attacker Yusuf Yazici pounced on a loose backward pass from McGregor and squared for Ikone to steer past Hazard from six yards.
The stand-in Hoops skipper, however, made amends three minutes later after referee Fabio Verissimo pointed to the spot when defender Domagoj Bradaric fouled the sprightly Jeremie Frimpong in the box.
The Scotland international confidently drove his penalty low in to the corner past Maignan.
Then Ewan Henderson made his first appearance of the season as replacement for Frimpong, who was unable to carry on.
Celtic took their confidence into the second half and the Ligue 1 outfit struggled to impose themselves on the match.
However, in the 61st minute McGregor turned a cross from defender Cheikh Niasse against his own post and behind for a corner which the home side defended.
Moments later, midfielder Turnbull had a chance when he was played in by defender Kristoffer Ajer but he could not get the ball out from under his feet and his shot was deflected past for another corner which came to nothing.
Lille's second equaliser came after Duffy was booked for foul on substitute Isaac Lihadji in the left-back position.
When Yazici's free-kick was only cleared to Weah, he fired low from 16 yards through a crowd of players and past Hazard.
But back came Celtic again and in the 75th minute Turnbull swept in a pass from Ajer from 12 yard to give Celtic the advantage once more.
In the 81st minute Lihadji missed his kick with only Hazard to beat as the Parkhead defence was cut open but Lennon's men were determined to hang on for a morale-boosting win, albeit they still finished bottom of their group.