David Lee, who along with Thomas was faced with trying to guard the much-larger O'Neal, led the Knicks with 25 points and 16 rebounds.
Knicks coach Mike D'Antoni got his first win against his former team. The Suns won 111-103 on Dec. 15 in Phoenix.
With the score tied 87-87 with less than 10 minutes left, Thomas scored seven points as the Knicks went on a 12-4 run. Robinson's 3-point play gave New York a 99-91 lead.
After a tip by Grant Hill pulled the Suns within 103-99 with less than three minutes to go, Chris Duhon gave the Knicks some breathing room with a 3-pointer to extend the lead to seven.
The Suns pulled within 112-109 on Jason Richardson's 3-ponter with 11 seconds left, but Al Harrington hit a pair of free throws to clinch the win. Richardson led the Suns with 27 points.
With less than four minutes left in the first half, Duhon fed Lee for a dunk over Amare Stoudemire that drew a foul. Stoudemire tripped over Lee's legs and stumbled toward the Knicks bench, where Robinson had come on the court and was pounding his chest in celebration. Stoudemire and Robinson bumped into each other, and Robinson was called for the technical foul for leaving the bench.
Steve Nash and Lee each hit their free throws, and the Knicks had a 52-46 lead. The Suns then ended the half on a 12-2 run.
The Suns attempted 21 free throws in the first half to the Knicks' eight, but made just 13. O'Neal, who came in shooting 62.8 percent from the line this season, was 4-for-9.
He finished with 21 points and 12 rebounds, making 8-of-16 field goals and 5-of-13 free throws.
Robinson's drive with six seconds left in the third quarter gave the Knicks an 84-76 lead, but Matt Barnes answered with a 3-pointer at the buzzer.
That started a spurt of eight straight points by the Suns to tie the score just over two minutes into the fourth quarter.
Robinson's points were the most he's scored since getting 20 on Dec. 28.
Notes: Knicks C Jerome James is scheduled to have surgery to repair a ruptured right Achilles' tendon Thursday. The injury occurred during practice on Sunday.
