It was the first time a player other than Emmanuel Riviere or Radamel Falcao had scored for Monaco this season.
Both teams hit the woodwork in the second half, with Reims goalkeeper Kossi Agassa doing well to push Layvin Kurzawa's fierce header onto the bar three minutes after the break.
Shortly after the hour mark, Floyd Ayite controlled a brilliant lobbed pass from around 60 yards (meters) and raced forward before unleashing a powerful effort which crashed off the crossbar.
Turan was sent off three minutes from full time for a second booking just 30 seconds after being shown a first yellow card for dissent.
Earlier, Montpellier was also held to a fifth successive draw, finishing up 1-1 with Ajaccio in Corsica in a match which both teams finished with 10 men. Newly-promoted Nantes won 3-1 at Rennes.
Filip Djordjevic opened the scoring in the 17th minute, firing in the rebound after he had headed Lucas Deaux's cross onto the left hand post.
Nantes doubled its lead two minutes from halftime when the ball came to Serge Gakpe, who did well to change direction, turn round his marker and fire a low shot across goal into the bottom right corner.
Nelson Oliveira pulled one back for Rennes 10 minutes after the interval, moments after Julien Feret had headed onto the post for the home side.
Deaux sealed the match in stoppage time.
It was the first time Rennes had conceded in five league matches.
In Corsica, Ajaccio got off to the worst possible start when midfielder Claude Goncalves was sent off in the ninth minute for what was harshly judged to have been a deliberate handball to clear Souleymane Camara's shot off the line.
Remy Cabella fired the spot kick powerfully and even though Ajaccio goalkeeper Guilherme Ochoa got his hands to it, he couldn't stop it from going into the top left side of goal.
The game changed in the 36th minute when Ronald Zubar headed Johan Cavalli's free kick down across goal and into the bottom right corner for the equalizer.
Moments later, Montpellier was also reduced to 10 men when Yassine Jebbour received a second booking following a poor tackle on Alessandro Crescenzi.
Ajaccio could have won the match in the last minute but Montpellier goalkeeper Geoffrey Jourdren pulled off a fantastic double save to keep out Paul Lasne's 20-yard attempt and then stop Aboubacar Camara's follow up.