A header from the Frenchman and a close-range finish from his teammate ensured Los Blancos are firm favorites to reach the quarterfinals of the Copa del Rey.
Benzema headed home in the first half following Luka Modric's cross before Jese turned home a second after halftime after Ronaldo teed him up. The victory puts Madrid in control of the tie ahead of the second leg against an Osasuna side that showed endeavor but struggled to pose any consistent threat to its hosts.
Madrid started with Jese, Ronaldo and Gareth Bale all behind Benzema, while Iker Casillas got the nod in goal ahead of Diego Lopez.
And it was youngster Jese who created the first moment of intrigue in the match, with the referee pointing to the spot after he was felled by goalkeeper Asier Riesgo, only to change his mind and issue a yellow card to the Madrid man for diving.
Madrid soon put the controversial moment behind it, as Modric swung in a free kick that Benzema headed home from 6 yards out.
Ronaldo twice fired wide from free kicks and Oier spurned a great chance as he scuffed a close-range shot, but the deficit remained at 1-0 until the second half.
A dreadful backpass from Oier handed Benzema the ball. He then played Ronaldo, who fed Jese in turn to allow the youngster to steer past Riesgo from inside the area.
Ronaldo missed a glorious chance for a third as he poked Modric's chipped pass wide before he later contrived to block Bale's goalbound effort and turn the ball past the post for a goal kick.
Osasuna struggled to make any inroads in the attacking third in the second half and ultimately Madrid cruised to a first-leg win without ever being fully stretched.