American Sweeting, who will face Japan's Kei Nishikori for the title, survived three break points in the fourth game and rallied from a 3-2 deficit in the tie breaker with five consecutive points to take the first set.
Sweeting broke Croatian Karlovic's serve to take a 4-2 lead over the 2007 champion in the second set and closed out the match on serve.
"I feel great here in Houston," Sweeting said. "Ivo had a three-hour match and was in a little bit of pain out here today.
I knew he'd be serving big, but you can't let that bother you.
You've just got to take care of your own serve.
"It's good to get to my first final here in the States and here in Houston."
In the other semi-final, Nishikori defeated Pablo Cuevas of Uruguay 6-3 7-5 to reach his second ATP Tour final. He won the Delray Open in 2008.
Nishikori dropped serve in the fourth and sixth game of the second set but recovered by breaking Cuevas in the fifth and 11th games. Nishikori's serve was nearly broken again in the 12th game but he fought off two break points to close the match with a forehand volley.
"I played great today, grinding away despite not being good on serve. It was tough conditions, hot and humid, but I battled through," said Nikishori, who can become Japan's highest ranked male player ever with a victory over Sweeting.
Nishikori is currently ranked 61st in the world, but would better Shuzo Matsuoka's career best of 46th if he defeats Sweeting.
"It's not like I can promise to win, but with the conditions in Japan I hope I can win tomorrow and give them a little bit of hope. It's always in my mind but when I play my match I have to concentrate."