Polansky beat two players ranked in the top 100 to qualify for the main draw and took that form into the first-round clash, working hard to frustrate his Japanese opponent in a tight opening set.
Nishikori eventually succumbed to persistent pressure from the world number 256, dropping the first set 6-4 thanks to a single break of serve.
A succession of fierce baseline exchanges saw the second set stay in the balance for 45 minutes, before Nishikori found his touch to level the match with a timely break.
With the pressure on in a deciding set Polansky finally wilted, falling 4-0 down to the 23-year-old thanks to a pair of quick breaks.
Much to the annoyance of 10,000 fans on court a relieved Nishikori held his nerve to close out the match, claiming a hard-fought 4-6 6-4 6-2 success in just over two hours.