The Japanese top seed set up a semi-final with treble Grand Slam winner Stan Wawrinka, who had his troubles before putting away Canadian Denis Shapovalov 6-4, 7-6 (7/4).
Nishikori won his 11th match of the season as he controlled Fucsovics in their first career meeting.
Asia's top player began the year with a 12th career title in Brisbane before suffering his only 2019 loss at the Australian Open against Novak Djokovic in an injury-hit quarter-final exit.
Fucsovics arrived in the Dutch port city after playing the Sofia final last weekend.
"This is one of the best that I've played, the second set was almost perfect," Nishikori said. "I feel like I'm improving with each match.
"I was making almost every ball."
Wawrinka leads the series with Nishikori 5-4, winning their last match in August at Cincinnati.
"Stan is a very good player, I'm glad to see him back from injury," Nishikori said. "I hope we can have a good match."
"He's got a great backhand and plays very aggressive, it will be tough."
Wawrinka, the 2015 champion in Rotterdam, was broken while serving for the match against Shapovalov, leading a set and 5-4.
As the set went into a tiebreaker, his resistance stiffened, with Wawrinka running out the winner on his second match point as the Canadian drove long.
"I feel relieved, happy, I was playing great," said the veteran Swiss.
- Monfils eyes 'revenge' -
"I couldn't find a way to close out the match, he started playing better. He was more aggressive and I was giving him too much time.
"But I'm happy to be in the semi-finals. There were a lot of tough and long rallies in the tiebreaker."
Daniil Medvedev ended Jo-Wilfried Tsonga's seven-match win streak when the Russian triumphed 6-4, 6-2.
Tsonga, ranked a lowly 140 after 2018 knee surgery, had been on a roll in the Dutch port city, following his title victory last week in Montpellier.
But fifth seed Medvedev arrived in Rotterdam buoyed by a title of his own after lifting the Sofia trophy five days ago.
Medvedev outlasted 33-year-old Tsonga in a 90-minute struggle to reach the semi-finals and a meeting with Gael Monfils.
The French showman took 69 minutes to advance to his second straight semi-final of the season with his 6-1, 6-2 thrashing of Bosnian Damir Dzumhur.
Medvedev improved to 14-2 this season after advancing with seven aces and saving both break points he faced against Tsonga who suffered only his third loss of 2019.
"The match felt strange, I don't think I was playing that well," said the beanpole Russian.
"Jo was probably not happy with his level, but that is normal. We've both played a lot of matches (in recent weeks). I'm just happy I managed to win today."
Monfils finished runner-up in Rotterdam 2016 to Martin Klizan and lost to Rafael Nadal in the 2009 title match at the Ahoy Arena.
Dzumhur had beaten third seed Stefanos Tsitsipas in the opening round.
After going down to Medvedev last week in the Sofia semi-finals, Monfils knows his priorities for Saturday.
"I'd like to take a bit of revenge," he said.