Mayo hit 8-of-12 field goal tries, including a pair of 3-pointers, and also notched eight assists and three rebounds.
Dallas shot 54 percent from the field as a team and scored 31 points in the fourth quarter to keep the 76ers at bay.
The Mavericks led 57-52 at halftime but were outscored 22-19 in the third quarter and led by 2 points at the start of the fourth.
2014: NFL Cheerleaders [PHOTOS]
Julius Randle breaks leg during NBA debut