The first was a 15-foot, fadeaway shot from just inside the key to tie it with 10.6 seconds left, the second a 21-footer from the baseline at the buzzer.
"I don't know whatever words you want to use, but he loves that moment," Knicks guard Jason Kidd said. "I'm trying to figure out if that last shot was tougher than the one before that he took."
The game winner came on an inbound pass from Kidd after the Suns turned it over with a second to play.
"It was premeditated," Smith said. "I was walking around the court going, 'You are going to make it, you are going to make it.' I was trying to get my form ready before I even thought about taking it. I was trying to go through my mechanics in my head, get my shoulders square to the basket and just let it fly."
Jared Dudley had a career-high 36 for Phoenix, including two free throws that put the Suns ahead 97-95 with 34.5 seconds to go.
New York was without the NBA's No. 2 scorer in Anthony (hyperextended knee) and Felton (finger), both hurt in the Christmas Day loss to the Lakers in Los Angeles.
The Knicks said X-rays on Felton's right fifth finger revealed a fracture and the next course of action will be determined after his return to New York.
"We just have to go back and assess it and see where we are and go from there, but again, like I said, injuries occur," New York coach Mike Woodson said. "Key guys get banged up here and there and we have enough guys on our team that guys just got to step up and play until guys get back. That's how it's got to be."
The Suns lost Goran Dragic in the final seconds of the first half when he was undercut by Smith on a layup attempt and fell hard to the floor. Dragic had bruises to his hip, back and wrist. Smith was called for a flagrant foul on the play.
Phoenix coach Alvin Gentry knew there was no intent to injure on Smith's part.
"J.R., he's not that kind of player," Gentry said. "He plays hard and he competes like crazy. It was an accident. It was one of those things that happens."
Dudley, whose previous high was 33, was 11-of-17 shooting, 5-of-8 on 3s, and 9-of-9 at the foul line. Marcin Gortat added 13 points for the Suns, who lost their third in a row.
New York led 54-44 at the half and stretched it to 68-54 when Smith made a fadeaway, falling-down 19-footer with 7:13 left in the third. Dudley responded with a 3-pointer and the Suns were off on a 20-4 outburst.
Another 3 by Dudley tied it at 72 with 2:10 to go, and Shannon Brown, who made just one of his first seven shots, scored on a fast-break layup to put Phoenix ahead 74-72 with 1:23 left in the quarter.
It was knotted at 76 entering the fourth.
Dudley was fouled by Copeland on a 3-point try and made all three free throws to put Phoenix up 90-86 with 5:19 left, but Smith scored the next four, Kidd sank a 3 and Copeland made a 21-footer in a 9-0 spurt that had the Knicks up 95-90 with 3:34 left.
After a scoreless 1:28, Sebastian Telfair made a 3, then Brown sank a 20-footer to tie it at 95 with 1:15 remaining.
Smith missed a jumper from the top of the key 52 seconds from the finish and the Suns got the ball. Dudley was fouled on a drive to the hoop and made both free throws to make it 97-95.
But Smith, with P.J. Tucker all over him, sank a fadeaway from just outside the free throw line to tie.
Gentry called a 20-second timeout, but the play broke down and, when Telfair tried to hit Gortat for a back-door layup, the ball was knocked back into the backcourt by Kidd. Telfair chased it down but wound up stepping out of bounds with a second on the clock.
After a timeout, Kidd tossed the pass to Smith, who got the shot off, again over Tucker, from just inside the 3-point line. It went in and he was mobbed by his teammates.
"It happened so fast, and obviously you want to keep it for the last shot and live with that," Dudley said, "but you give them one second and J.R. with the big shot."
The Knicks complete their brief three-game trip west at Sacramento on Friday. ... New York has lost two in a row only once this season. ... Michael Beasley, a big part of the second-half surge, missed Sunday's home loss to the Clippers due to illness. ... The 36 points were the most by a Suns player in two seasons. ... Kidd also had eight assists and six rebounds. ... New York also was without Rasheed Wallace with a sore left foot. .... It was the first time the team had been without Anthony and Felton in the same game. .... The Knicks are 3-2 without Anthony.
Goorjian breaks down Giddey's talent & Tokyo squad decision
Brian Goorjian joins Ball and the Real World to discuss the tough call not to include Josh Giddey in the Tokyo squad, and how important he is to the Boomers' future.
Exum was 'fearless' in Tokyo
Boomers coach Brian Goorjian heaps praise on the ferocious, determined way in which Dante Exum played and practiced during their Olympic campaign.
Giannis Antetokounmpo in Greece as mom, brother handed citizenship
NBA star Giannis Antetokounmpo was in Greece for a meeting with the country's prime minister Thursday and a special ceremony to bestow Greek citizenship on his mother, Veronica, and younger brother Alex.