Randolph's performance was the 11th 20-20 game in Memphis franchise history and helped the Grizzlies to their fifth win in seven games. Darrell Arthur and Rudy Gay also hit double figures for Memphis.
Nowitzki, who had missed nine games with a knee sprain, scored seven points with five rebounds in 15 minutes of play before being ejected in the third quarter after being called for a foul against Randolph and then a pair of technical fouls.
Dallas got 17 points from Ian Mahinmi but were done in by a 32.4 percent shooting performance that going 6-of-31 from 3-point range.
The Mavericks have lost five in a row for the first time since Nov. 7-14, 2008.