The British number two's 6-3 3-6 6-4 win was his first at the Bercy event and set up a showdown with Greek world number five Stefanos Tsitsipas on Wednesday.
Evans broke for 2-1 in the opening set and took his first set point on the Nakashima serve when the world number 50's backhand drifted wide.
American Nakashima converted his first break point of the match to take the initiative at the start of the second.
Evans saved three break points to stay in it at 3-4 but Nakashima took his third set point to force the decider.
However, 32-year-old Evans began to dominate at the net again and a couple of crisp volleys secured a break for 3-2.
Two match points came and went on Nakashima's serve but Evans finished the job on his own to wrap up victory in two hours and nine minutes.
Jack Draper also progressed after a straight-sets win over French wildcard Arthur Rinderknech.
The 20-year-old, ranked 45th in the world, won 6-3 6-4 in just over an hour-and-a-half.
British number three Draper will next play 16th-seeded American Frances Tiafoe, the world number 21.
Elsewhere, ninth seed Andrey Rublev became the first player to reach the third round with a 6-2 6-3 victory over John Isner, breaking the American twice in the first set and once more in the second.