Six players scored in double figures for the Suns, who won for the second time in three games.
Shawn Marion had 16 points, Grant Hill scored 14 and Steve Nash added 12 points and seven assists for the Suns, who shot 61.5 percent from beyond the 3-point line.
Phoenix was again without Amare Stoudemire, who is recovering from offseason arthroscopic surgery on his right knee.
Carlos Boozer, making his first appearance after missing most of training camp while tending to his ill son, scored 10 points on 5-of-7 shooting in 13 minutes for the Jazz (2-2), while Paul Millsap had 16 points and Ronnie Brewer added 15.
Utah led by four points in the opening minutes but the Suns took the lead for good at 16-14 on a fastbreak layup by Barbosa with 3:37 to play in the first quarter.
Bell, who was 5-of-6 from the 3-point line and 8-of-10 from the field, scored 21 in an 11-minute span of the second and third quarters as Phoenix extended a seven-point lead to as many as 35.
Millsap's dunk pulled the Jazz within 42-35 with 5:27 left in the first half, but Bell hit two 3-pointers and scored eight points to key a 16-6 run as Phoenix opened a 58-41 halftime lead.
Bell scored 13 points as the Suns opened the third quarter on a 22-9 run to take an 80-50 lead with 6:50 remaining in the third quarter.