Goran Dragic had 13 points and six assists for the Suns, who won two of their last three.
The Suns capitalized on poor Denver shooting to extend a five-point halftime lead to 62-51 on an 18-foot jumper by Beasley with 5:07 left in the third quarter.
The Nuggets were 4 of 22 from the floor in the period and scored just 11 points. Phoenix only was slightly better at 7 for 24, but the difference was enough for the Suns to carry a 67-57 lead into the fourth.
Phoenix led by as many as 18 in the final quarter.
Beasley finished 13 of 21 from the floor, including 3 for 3 from beyond the arc, and added 10 rebounds. The rest of the Suns shot 34.8 percent (23 of 66).
Denver, which lost its fourth straight, had 31 field goals and 26 turnovers.
Beasley scored eight straight points in the second quarter as the Suns rallied from a 37-34 deficit to take a 41-39 lead with 4:39 left in the first half. Beasley added a running 5-footer and Dragic hit a pair of free throws to put Phoenix ahead 51-46 at halftime.
DeMar DeRozan, arguably the top shooting guard who could hit the free-agent market, is focused on re-signing with the Raptors, a source said.
Cavaliers point guard Kyrie Irving has accepted an invitation to play for Team USA at the Summer Games, filling out the 12-man roster for Rio de Janeiro.
Heat president Pat Riley said re-signing Whiteside will be the team's No. 1 priority, with a max contract projected to be $94.8 million over four years.