Dallas native Darrell Arthur scored 11 of his 17 points during a 20-11 third-quarter run that gave the Grizzlies a 74-69 edge. Arthur sat out the first two preseason games due to a strained pectoral muscle.
The Mavericks carried an 82-81 lead into the fourth quarter.
Humphries did all the scoring during Dallas' 9-0 run late in the second quarter and the Mavericks built a 56-50 halftime lead.
Mavericks swingman Josh Howard has yet to play in the preseason as he completes his recovery from offseason left ankle surgery. Howard continues to do some running, and should begin participating in 5-on-5 scrimmages soon, with the goal of playing in one of Dallas' final preseason games.
Dallas' Tim Thomas has also missed the first three preseason games after right knee surgery.
Allen Iverson, who signed a one-year free-agent deal with Memphis on Sept. 10, is expected to be out three more weeks with a partially torn left hamstring.