Jodar extended his remarkable first season on tour with a composed win over Fils.
He earned an early break, but Fils fought back before rain suspended play again with the Frenchman serving to stay in the first set.
Jodar took the opener in the tiebreak after the restart and carried his momentum into the second set, breaking three more times to secure the victory that will lift him to at least 11th in the rankings.
It was the 34th win of the Spaniard's incredible breakthrough year.
Nakashima sent over 11 aces and offered up a subdued celebration for the career-breakthrough win in Montreal.
Nakashima, seeded 28, converted a break point in the fourth game before breaking his opponent to love to close out the first set, as the visibly frustrated Darderi's composure unravelled.
Darderi dug in his heels in the second set but could only hold off the determined Nakashima for so long, as the American broke him on the fourth try in the penultimate game.
Nakashima sent 19th-seed Darderi skittering around the court in the final game, forcing him into an error at the net on match point and pumping his fists in celebration after the customary post-match handshake.
