After the Catalans had beaten Getafe 1-0, champions Madrid won a tight clash at the San Mames to remain three points behind their rivals.
Benzema broke the deadlock with a superb volley in the first half while Kroos fizzed home the second late on to kill off Athletic’s hopes.
After losing the Spanish Super Cup to Barcelona last weekend, anxiety had increased in the capital, but a stirring Copa del Rey comeback against Villarreal on Thursday settled nerves.
This victory in Bilbao will reassure Los Blancos fans further, ahead of their derby clash in the cup with Atletico Madrid next week.
Anticipating a physical clash with the Basques, Carlo Ancelotti benched midfield stalwarts Luka Modric and Kroos, opting to line up with Eduardo Camavinga and Fede Valverde as part of his central trio.
Dani Ceballos, Nacho Fernandez and Marco Asensio also started after their fine performances against Villarreal.
Athletic started well and Madrid goalkeeper Thibaut Courtois tipped away Aitor Paredes’s dangerous header.
The goalkeeper forced Inaki Williams wide of goal in the 23rd minute and the Ghana international fired into the side netting from a tight angle.
A minute later and Madrid punished him for the miss, with Benzema reacting well to volley home from Asensio’s header back in his direction.
In the second half Unai Simon was called into action to deny Nacho as Madrid sought to double their lead, with Asensio dragging a shot narrowly off-target.
At the other end Nico Williams followed suit, firing wide when well-placed.
Athletic continued to turn the screw in their search for the equaliser with Ernesto Valverde throwing on more attacking players, including captain Iker Muniain.
Inaki Williams found the net in the 77th minute but the goal was swiftly ruled out for offside against Gorka Guruzeta.
Eventually the hosts were finished off by Kroos, who steered home from the edge of the box to wrap up Madrid’s victory.
Athletic sit eighth, five points below the Champions League qualification spots.