With the win, the 35-year-old American reached his third career ATP Tour semifinal and first since Newport in 2013.
Russell, who lives in Houston, needed an hour, 48 minutes to finish off the former world No. 1, and he finally beat Hewitt after being broken with two double-faults when serving for the match up 5-4. Russell also failed to convert a couple of match points in the tiebreaker before winning.
"Every time we play it's a battle," Russell said. "It's kind of the mentality knowing, `Yeah, you're serving it out. But this guy has a really good return.' And vice versa the same thing when he's serving. He knows I'm not going to give him any free points usually, so it's almost a mental battle between the two of us. I'm just really pleased to get through."
Russell will play defending champion Kei Nishikori on Saturday. The top-seeded Nishikori rallied to beat Russian Alex Bogomolov Jr. 3-6, 6-3, 6-2 earlier Friday. Fourth-seeded Lu Yen-Hsun of Taiwan beat American qualifier Alex Kuznetsov 6-1, 6-4 and will play Ivo Karlovic of Croatia, a 7--6 (4), 6-7 (3), 6-3 winner over American Jack Sock.
Both Russell and Hewitt struggled with their serves with each double-faulting six times in the match. Hewitt double-faulted on break point serving in the first game of the second set. Hewitt needed three sets to win Thursday night in his first match here, and he said his shoulder flared up a bit afterward.
"My rhythm on my serve wasn't there," Hewitt said. "I was feeling my shoulder a little bit and just couldn't hit my spots. So that was putting me under a lot of pressure then, and he makes a lot of balls and makes you play a lot."
Russell didn't manage a point off his serve trying to close out the match up 5-4. Hewitt held serve to send the set into the tiebreaker where Russell went up 6-4 when Hewitt put a backhand into the net. Serving for the match, Russell hit his own forehand into the net. Hewitt stayed alive for another point with a brilliant forehand down the line into the corner to tie at 6.
But Hewitt hit a forehand wide and then a return long as Russell advanced to his third semifinal -- all since Houston in 2012 with each on a different surface.
Karlovic, with five career titles, served up 16 aces in knocking the 21-year-old Sock out of his second quarterfinal this year. Karlovic needed 2 hours, 25 minutes, and he finally got the edge in the match by breaking Sock to go up 2-1 in the third. Karlovic converted only one break point after failing on his first 10 chances. He finished the match by breaking Sock again.
Bogomolov broke Nishikori for a 3-2 lead in the second set only to be broken on his next two serves, and Nishikori served out to take the set. In the third, Nishikori fought off three break points to hold serve and broke Bogomolov in consecutive games to take a 5-2 lead.
"Obviously, he was playing really well I thought," Nishikori said. "He was hitting ball really flat and deep and wasn't making mistakes, especially from the beginning he was very aggressive. I wasn't maybe playing 100 percent. From the second set, I start playing little more aggressive and playing better. ... It wasn't easy but I'm glad to stay strong and to win in three sets."
Lu, who lost in the final in Auckland, reached his second semifinal in four events this year by beating a qualifier making his first career appearance in an ATP Tour quarterfinal. He made quick work of the first set and was up 3-1 in the second before Kuznetsov tied it up at 4-4. Kuznetsov double-faulted as Lu broke his serve for the match.