It was the seventh straight home loss for the Knicks, who haven't won at MSG since beating Philadelphia on Nov. 22. New York has lost four straight overall and is 5-24.
"I can just see it out there on the court, that we don't believe in ourselves to be able to go down the stretch and win basketball games," Carmelo Anthony said.
Markieff Morris added 19 points for the Suns, who won their second straight after a six-game skid. They got 57 points from their point guard trio of Bledsoe, Thomas and Goran Dragic.
"That's the strength of our team," Thomas said. "When we're playing at a high level that gives us the best chance of winning."
Thomas made a 3-pointer to open the fourth quarter, giving Phoenix the lead for good and triggering an 8-0 burst. Marcus Morris made another and Alex Len tipped in a miss for a 75-68 lead, and the Knicks were playing catch-up from there.
Anthony had 25 points and 11 rebounds for the Knicks after missing a game with a sore left knee, but he was on the bench for a rest when the Suns surged into the lead in the 3:18 before he re-entered.
"There's really no excuse for that," Knicks coach Derek Fisher said. "That group that started the fourth quarter, we talked about if we win the fourth quarter, we win the game, and those first few minutes of the fourth quarter were probably the worst stretch of the game."
Jose Calderon added 21 points for the Knicks, who rested Amare Stoudemire while already playing without the injured Iman Shumpert and J.R. Smith.
New York got within three points heading into the final 3 minutes, but Thomas made a free throw, Markieff Morris nailed a jumper and Thomas followed with a 3-pointer, pushing the lead to 95-86 with 1:34 to go.
"Carmelo for that stretch there, I don't know what he scored, three or four straight times. You're going, `OK, he's going to be a handful in there,' and that's the time of the game that he likes to get going," Suns coach Jeff Hornacek said. "But again, every time we seemed to match it with something."
Phoenix burst out to a 15-4 lead midway through the first quarter before Calderon steadied the Knicks with a couple of 3-pointers. New York cut it to three after one and surged to a seven-point lead in the final minute of the second before taking a 47-44 advantage to halftime.
Markieff Morris then scored 12 in the third quarter to keep Phoenix within a point headed to the final 12 minutes.
Suns: Phoenix is 6-1 on the road against Eastern Conference teams. ... Markieff Morris, who picked up two technical fouls and was ejected from Wednesday's loss in Charlotte, got called for another after the first half ended Saturday. Anthony shot it before the second half started.
Knicks: The Knicks were playing the first of three straight day games. They visit Toronto on Sunday afternoon and are home to face Washington in a noon tip on Christmas. ... Shumpert said he doesn't need pain medication for the shoulder he dislocated Dec. 12 at Boston, just ice. The Knicks said after the injury that he would be re-evaluated in three weeks.
Bledsoe and Thomas carried the load while Dragic shot just 4 for 11, but Thomas knows it can go another way the next game. "We know that one night it might not be your night or it might be your night, just go out there and play the same way," he said.
AND NOT MUCH BETTER ON THE SECOND NIGHT
The Knicks fell to 0-7 on the first night of back-to-back games. They are 1-5 on the second.