Rennes, who have never won the French championship but are making a surprise title bid under charismatic Corsican coach Frederic Antonetti, moved a point above Lille ahead of their home game with title rivals Olympique Lyon on Sunday.
Togo striker Boukari fired into the top corner after a fortunate ricochet on 14 minutes and the club from the north west of France, ninth last term, never looked back.
"It took us 10 minutes to get into the game but then we played well," Antonetti, who looks more like a rugby player than a soccer coach, told reporters.
"It's necessary to concentrate on our next match (at Montpellier) because everything will be decided on the field. Football fiction doesn't interest me."
In Saturday's other Ligue 1 games, third-bottom Monaco went 2-0 up thanks to Park Chu-Young's brace but drew 2-2 at home to Caen while bottom side AC Arles-Avignon stay 15 points from safety after being held 1-1 by Stade Brest in Provence.
Bordeaux ultras entered 15 minutes late in protest at the 2009 champions' poor form, which led assistant coach Michel Pavon to leave in midweek, but Alou Diarra's goal, a dubious penalty from Anthony Modeste and Jaroslav Plasil's superb curler settled matters.
Nice eased their relegation fears and further hit faltering Saint Etienne's push for the Champions League places with a surprise 2-0 win at Les Verts.
Sochaux and sixth-placed Montpellier drew 0-0 with a red card apiece and FC Lorient's trip to Valenciennes also ended in stalemate.
