Nishikori did not face a break point in the match and leaped from a 2-2 tie in the first set.
Fish, the top-ranked American at No. 11 in the world, won only one more game the rest of the set.
"I don't think he played great today, he was missing a lot," Nishikori said. "But I played good enough to beat him and played good clay-court tennis."
"I was hitting good returns," Nishikori said. "That's one of the things I did great today."
A title in Houston would have vaulted Fish into the ATP top 10 rankings.
"Being the No. 1 American, it's a responsibility every time you step on the court, people would say, 'I'm going to go and watch so and so today and have a pretty good experience doing it,'" Fish said.
"That's a responsibility hopefully I'll have for a little bit and do a better job of it than I did tonight."
The 6-foot-10 Karlovic -- the tallest player on the ATP Tour -- is accustomed to using his height for a good service advantage but felt he was looking in a mirror against the 6-9 Isner, who had 23 aces.
"Now I know what it's like to play me," Karlovic said. "It's really not easy. I was trying to stay confident even if he was acing me left and right. I tried to stay calm and in the end, I don't know what to say, I was a little luckier. It was a close match."
Isner, who played a match that lasted more than 11 hours against Nicolas Mahut at Wimbledon last year, played a later doubles match.
Tied at 9-all in the final tiebreak, Karlovic slammed home his final ace and ended it with a forehand drive that clipped the line.
Isner looked hopeful that the shot was out but the ruling stood.
"I knew it was in because I saw it skid," Karlovic said.
The match was that close throughout. There were only two service breaks in the match and those were back to back in the 11th and 12th games of the second set to force the second tiebreak.
Karlovic, the 2007 champion, missed much of last season following Achilles tendon surgery. He has played six matches in seven days, including three qualifying matches and three in the main draw.
Karlovic sympathized with Isner, a one-time doubles partner.
"It's not easy to lose like this," Karlovic said. "It's all about one point here and there but it was a good match and I wish him all the best in the coming weeks."
Sweeting, who earlier upset No. 2 seed Sam Querrey, had to overcome a slow start.
"It's a tremendous goal to get to the semifinals, it's my first one," Sweeting said. "I tried not to let the pressure get to me on the court and stayed calm and focused and I think that's a sign of maturing a little.
"Usually, I would panic a little closing out the match. Now, I also want my first final and my first win," he said.