Carter scored 15 of his 37 points in the pivotal third quarter to help the Nets rally from a 19-point deficit to defeat the Boston Celtics, 102-93, and clinch the eighth and final Eastern Conference playoff spot.
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Rookie Nenad Krstic collected 18 points and 10 rebounds and Jason Kidd added 19, eight and seven assists for New Jersey (42-40), which finished tied with Cleveland in the standings but won three of their four matchups to own the tiebreaker.
The Nets won 15 of their last 19 games and will face top-seeded Miami in the first round of the playoffs. They went 47-35 last season before falling to eventual champion Detroit in the Eastern Conference semifinals.
New Jersey trailed, 49-30, after a 3-pointer by Boston's Paul Pierce with 5:07 left in the second quarter.
"I didn't even know we were down by 19," Kidd said. "That's how much I was paying attention to the score."
"I'm happy that we didn't hang our heads," Carter said. "We kept knocking down the lead bit by bit. We could have said this could be over but we didn't."
The Nets pulled within 58-47 at the break, then opened the second half on a 22-6 run, taking a 69-64 edge on a 3-pointer by Brian Scalabrine with 4:12 remaining in the period.
"Our halftime was kind of silent," Scalabrine said. "Coach got on us and explained the situation. He basically said that we had 24 minutes for our life. This was our season."
The Nets pushed their advantage to 79-66 entering the fourth quarter - outscoring Boston by a whopping 32-8 in the third - before the Celtics' reserves made things interesting, climbing within 96-93 on a jumper by rookie Justin Reed with 1:16 left.
But the Celtics were blanked thereafter, and Kidd, Scalabrine and Travis Best combined to go 6-of-8 from the line in the last 71 seconds for the final margin.
"It's a great feeling," said Carter, who was acquired from Toronto in December. "We've accomplished a lot. My goal was just to come in here and lend a helping hand. It's one thing to want to be in the playoffs, but it's another thing to play like a playoff team."
Pierce scored 19 of his 21 points in the first half for third-seeded Boston (45-37), which faces either Indiana in the playoffs. As expected, Boston coach Doc Rivers benched his starters for the fourth quarter.
"I think our guys are in the right frame of mind now," Rivers said. "I thought our veterans had been playing not to get hurt and that's when you get hurt. You could see it on a lot of the rough rebounding, and that's when I figured I'd go with the young guys."
Boston went 36-46 last season before getting swept in the first round of the playoffs by Indiana.