Joao Moutinho's fine free-kick got the visitors back on level terms in the 13th minute, cancelling out Antoine Devaux's fourth-minute header, but they could not force a winner - despite the 87th-minute dismissal of Reims defender Atila Turan.
Both goalkeepers pulled off some fine saves in the second half to ensure the spoils were shared, meaning Monaco finished the weekend top of the pile.
Despite hitting back with a second-half Nelson Oliveira strike, the hosts suffered defeat at home for the first time this season thanks to goals from Filip Djordjevic, Serge Gakpe and a late Lucas Deaux strike - the first time Rennes had conceded in four matches.
Ajaccio and Montpellier remain languishing in the bottom half of the standings after battling out a 1-1 draw at the Stade Francois Coty in a match which saw both sides reduced to 10 men in the first half.
The hosts had midfielder Claude Goncalves sent off in the eighth minute for deliberate handball and Remy Cabella made no mistake from the resulting penalty to give Montpellier the lead.
Ronald Zubar equalised for Fabrizio Ravanelli's side in the 36th minute, though, and then Montpellier defender Yassine Jebbour saw red for a second bookable offence two minutes later.