The world number six, who has never progressed further than the fourth round at SW19, sealed a 6-4 6-3 7-5 victory over his Australian opponent.
Groth faced a test from the off as he was forced to hold off a break point in his opening service game, but Nishikori kept knocking on the door and eventually went a break up to take a 3-2 lead.
Nishikori maintained his advantage as he took the first set in 40 minutes, but he suffered a slight wobble when Groth broke back immediately after losing his serve at the start of the second set.
The Australian Open quarter-finalist was able to recover, though, as he broke twice to double his lead, but Groth continued to cause some problems.
Once again, the 28-year-old broke back in the third, but Nishikori bounced back with a break of his own to wrap up the match.