The Cavaliers, who set the record for consecutive losses in one season at 24 when they fell to the Portland Trail Blazers on Saturday, had a chance to tie the game against Dallas in the final seconds but Anthony Parker missed a three-pointer.
"When it hit the front of the rim, I still thought it was going to hit the backboard and trickle in," Parker said. "It is disappointing to come up short again. We just have to keep at it."
Cleveland (8-44), whose last win came on December 18 over the New York Knicks, play their next eight games at home, where they have recorded five of their wins this season.
J.J. Hickson put up 26 points and 12 rebounds while Ramon Sessions added 19 points and 13 assists to help Cleveland put up a good fight against Dallas.
The Cavaliers fell behind by 15 points during the second quarter but clawed back to tie things early in the fourth and take the game down to the wire.
Dallas reserve Jason Terry finished with 23 points to rally the Mavericks (36-15).
The Cavaliers posted the NBA's best record last season, but things took a downturn when two-times reigning NBA MVP LeBron James signed with the Miami Heat during the offseason sending the franchise into a freefall.