Mayo had 18 points despite 3-of-14 shooting because he was 12 of 13 from the line. Shawn Marion also had 18 points to go with nine rebounds, while Brand had 11 points, 10 rebounds and two blocks.
Six Mavericks finished in double figures for the second straight game, but Dallas was looking to Nowitzki in key stretches. He hit a 3-pointer late in the third quarter to stem a Houston rally and had another big jumper after Lin pulled the Rockets within a point with 3:40 left.
"I had some good looks," said Nowitzki, who has scored in double figures in nine straight games after a slow start in his return from knee surgery that sidelined him for the first two months. "That 3 at the end of the third helped me get my rhythm. Sometimes all you need is to see the ball go through the hoop one time."
The Mavericks shot 38 percent and had a subpar night at the line before Nowitzki, Mayo and Dahntay Jones combined to make eight straight in the final 1:02.
Harden had gone more than two quarters without a basket when he stole a pass and converted a three-point play on the other end midway through the third. He ended up with five points during a 10-2 run that pulled Houston to 71-69.
NOTES: The Mavericks didn't trail in Monday's 113-98 win over Minnesota, the first time this season Dallas led from start to finish. It also was the first time the Mavericks had three players with 20 or more points in a game. Darren Collison scored 23 and Mayo and Brand added 20 apiece. ... Collison and Mayo had nine assists each against the Timberwolves, making it the first time since 2002 that two Dallas players had at least 20 points and nine assists in the same game. ... Houston's 18 points in the first quarter matched a season low for a Dallas opponent in the first. ... James' 10-day contract expires at midnight Thursday. He played critical minutes against the Rockets, increasing the likelihood that he'll stay around.