Fifth seed Nishikori completed a 7-5 6-4 6-4 win over Brazilian Thomaz Bellucci.
Bellucci fought hard in the first set, fending off multiple break points, but the pressure finally told and Nishikori was able to go one set up.
The Japanese star then won the first four games of the second set, and despite a spirited fight back, it was always going to be hard for Bellucci from there.
Nishikori moves on to face Benjamin Becker in round three.
Fourth seed Berdych defeated his countryman Radek Stepanek 6-3 6-7 (7-9) 6-3 6-3.
Berdych converted five of 14 break points in the four-set encounter, and saved eight of the nine break points he faced on serve.
A couple of French seeds also advanced on Wednesday, much to the delight of their home crowds.
Gael Monfils, seeded 13th, needed five sets to get past Diego Schwartzman 4-6 6-4 4-6 6-2 6-3, while 14th seed Jo-Wilfried Tsonga dispatched Dudi Sela 6-4 6-1 6-1.
A couple of seeds were on the receiving end of defeats, with 24th seed Ernests Gulbis going down 6-3 3-6 7-5 6-3 to Nicolas Mahut and 28th seed Fabio Fognini losing 6-1 6-3 7-5.
Spanish 19th seed Roberto Bautista Agut was also bundled out, beaten 6-4 6-2 6-2 by Lukas Rosol.