Kyrie Irving scored 12 of his 23 points in the fourth quarter and the Cavaliers snapped a four-game losing streak with a 110-101 victory on Wednesday night.
Bledsoe, who underwent knee surgery and missed 33 games, had 15 points on 5 for 16 shooting and a team-high nine assists in 32 minutes.
"It spoiled everything," he said of the loss. "It was a team we needed to beat and a game we needed to win, so now it's going to make it that much tougher."
Irving also had nine rebounds and six assists for the Cavs, who never trailed, building a 14-point first-quarter lead.
"They looked like the team that was trying to get into the playoffs," Phoenix coach Jeff Hornacek said. "We looked like the team that just wanted to play a basketball game."
Phoenix fell two games behind Memphis and Dallas for the final two playoff spots in the West.
The Cavaliers led by as many as 20 at home before falling to Phoenix earlier this season. But they held off a Phoenix rally this time.
"A lot of huge contributions from a lot of our guys, especially from the three-point line," Cleveland coach Mike Brown said.
Cleveland led by 15 in the opening minutes of the third quarter but the Suns, behind Dragic's 11 third-quarter points, cut it to two twice late in the period, the last time on Gerald Green's 11-footer in the lane that made it 77-75 with 35.9 seconds left.
But after the teams traded baskets, Dion Waiters made a 3 at the buzzer to put Cleveland up 82-77 entering the fourth.
It was part of a 12-2 run that gave the Cavaliers an 89-77 lead on Irving's 18-footer with 10:15 to play.
Green's steal and breakaway dunk cut it to 89-81, but Irving scored eight, including two 3s, in a 9-3 spurt and the Cavs led 98-84 with 6:33 left.
Green, who had averaged 26 points in his previous five games, scored eight on 4 of 14 shooting, 0 for 6 from 3-point range as the Suns went 10 for 36 from beyond the arc to Cleveland's 12 of 24. The Cavs outrebounded Phoenix 51-36.
The Suns also struggled from the foul line, going 13 of 22 to Cleveland's 22 of 27.
Hawes scored 17 in the first quarter, including 3 of 3 3-pointers, as Cleveland took a 37-24 lead.
"They were sinking back and just letting me walk into some on the trail so I took advantage of that," he said.
It was the highest-scoring first quarter of the season for the Cavaliers.
"I don't know what it is with us in these first quarters," Dragic said. "We played better (after that) but you use up so much energy trying to come back."
Phoenix never got closer than nine in the second quarter. Markieff Morris scored inside to make it 46-37, but Tristan Thompson made a 6-footer and Deng made a 3 and Cleveland led 51-37 with 4:01 left in the half.
The Cavs were up 60-47 at the break, outrebounding the Suns 25-13 and making 8 of 11 3s to Phoenix's 5 of 18 in the first two quarters.
The Cavaliers signed F Shane Edwards to a 10-day contract and released F Arinze Onuaku. ... The game was the only one at home for Phoenix in a stretch of six. ... Hawes was called for a flagrant foul on Miles Plumlee in the third quarter. ... Phoenix has lost seven of 10. ... Cleveland shot 47 percent, ending a string of seven straight games in which the Phoenix opponent shot better than 50 percent. ... The Cavs have won five of their past seven against Western Conference teams. ... Cleveland had lost four straight to the Suns.