Sporting again dominated possession and shots in front of their home fans but had to settle for a point after the Red Bulls' Bradley Wright-Phillips had cancelled out Toni's opener.
The visitors were lucky to only trail by one goal at half-time, having cleared two shots off their goal-line and watched Benny Feilhaber hit the bar with a free-kick, all in the opening 10 minutes.
But with Wright-Phillips scoring his 10th goal in seven matches, New York snapped a three-game losing streak and moved within a point of the play-off positions in the Eastern Conference.
The Red Bulls rose to 15 points in sixth with fifth-placed Columbus Crew just ahead on 16, while Sporting (19) sit second in the East.
Sporting entered Tuesday's game without a win in three games, having thrown away a late 2-1 lead in their draw with Toronto FC on Friday, while the Red Bulls had lost 2-1 at home to Portland Timbers on Saturday.
The hosts blitzed the Red Bulls early, forcing Ibrahim Sekagya and Jamison Olave into goal-line clearances in the opening four minutes, before Feilhaber struck the woodwork in the fifth.
Kansas City deservedly hit the front in the ninth minute when Feilhaber found Toni in the right channel and the Spanish forward drifted inside before curling his shot inside the far post.
Sporting had the ball in the back of the net again in the 25th minute after Kevin Ellis knocked the ball out of the hands of Luis Robles but the goal was disallowed for a foul on the Red Bulls goalkeeper.
At half-time, Sporting had taken eight shots, while the visitors had only managed one, and the home side would pay for their wastefulness when New York equalised five minutes after the break.
Red Bulls skipper Thierry Henry pierced Sporting's defence to release Wright-Phillips on the left and the Englishman slid his first-time shot under Eric Kronberg to make it 1-1.
Wright-Phillips almost claimed a brace three minutes later but his shot on the counter-attack was smothered by Kronberg, who burst off his line to make the save.
Sporting finished the match with 13 shots to New York's eight, while the home team also claimed 53.5 per cent possession, but were unable to register a victory.
With Sporting failing to win again, Eastern Conference leaders New England Revolution could stretch their advantage seven points with a victory at the East's bottom club Montreal Impact on Saturday.
