Modric curled in a brilliant strike to give Real a first-half lead at Riyadh’s King Fahd International Stadium.
Benzema then made it 2-0 with a penalty after the video assistant referee awarded a spot-kick for handball.
The striker’s shot had hit Yeray Alvarez, whose arms were raised as he made the block.
Real were also penalised for a handball late on as Eder Militao was sent off for blocking a shot and Bilbao were awarded a penalty.
However, keeper Thibaut Courtois produced a superb save to keep out Raul Garcia with his leg to ensure there was no late comeback for Athletic, who won the trophy last year.
Victory means Real move to within one of rivals Barcelona’s record tally of 13 Super Cup titles.