The winger inspired the Ligue 1 powerhouses to a routine victory despite the absence of attacking star Radamel Falcao
James Rodriguez and Anthony Martial netted a goal apiece, their first for les Rouge et Blanc, to fire Claudio Ranieri's men within two points of champions Paris Saint-Germain at the summit of the table.
Concerns arose over how the side would cope without star striker Radamel Falcao, with the Colombian ruled out with a thigh problem, but compatriot Rodriguez rifled home from a free kick in the 19th minute to allay any fears over the hosts' attacking prowess.
The winger was in full flow and nearly racked up an assist minutes later when he released Joao Moutinho to fire wide of Benoit Costil's goal.
Rennes' custodian then produced a reflex save to thwart Rodriguez, when the 22-year-old thumped a fierce volley on target after Jeremy Toulalan put him through.
Despite the home side's domination, the clincher only came before the stroke of half-time. Rodriguez slipped in Martial - Falcao's replacement on the night - allowing the starlet to register his first goal since moving to Stade Louis II with a deflected attempt.
Rodriguez was unlucky when a goalline clearance prevented him from adding to his tally, while an inspired Costil was key to preventing Monaco from running riot with stunning stops from both Lucas Ocampos and Emmanuel Riviere in the second period.
Ultimately, the Frenchman's efforts were in vain, and the victory ensures Monaco stay within touching distance of PSG, who host Olympique Lyonnais on Sunday. European hopefuls Rennes, meanwhile, sit 11th.