Instead, the Red Bulls scored a pair of second-half goals - with the Union playing a man down - to take a 3-2 win Sunday at PPL Park in Chester.
The Red Bulls have won four consecutive matches and moved into first place in the Eastern Conference with 22 points. New York (7-3-1) overtook Sporting Kansas City, which lost to Chicago, 2-1, on Saturday and has 21.
Pajoy now has three MLS goals on the season and has scored three goals in the last two matches overall. The Colombian import scored in the Union's 2-1 win against Germany's Schalke 04 Wednesday.
Pajoy brought the Union even in the 31st minute, finishing off a beautiful cross from Freddy Adu.
That was the highlight for Adu, who obtained a yellow card in the sixth minute and picked up a second just before halftime, after his stumble in the box was deemed a dive. That forced the Union to play a man down and will mean Adu cannot play Saturday at FC Dallas.
"I had a yellow card already, I'm not going to be stupid and try and dive," a frustrated Adu said after the match. "I was actually off-balance and was trying to lift my foot up and plant it in front of [the two defenders], and I just didn't get there. I didn't put my hands up. I wasn't looking for a call, but this referee saw it that way. It's unfortunate because we were having a great game and I feel like I blew it for our team."
Pajoy's first goal nullified a 17th-minute rip from Red Bull midfielder Joel Lindpere.
Less than one minute into the second half, Pajoy got his second as a cross from Danny Mwanga took a deflection off New York defender Brandon Barklage. Pajoy pounced, New York goalkeeper Ryan Meara flinched, and the Union took the lead.
Try as the Union (2-6-1, seven points) might in the second half, a game-tying goal appeared elusive despite numerous chances. The biggest came in stoppage time when a Michael Farfan free kick found Pajoy's feet directly in front of net, but Meara was there to gobble up the chance.
Califf on trading block?
At the end of the Union's Sunday matinee with the Red Bulls, Danny Califf was still a member of the franchise.
That might not be the case by the time you read this.
The Union has entertained a pair of offers from Chivas USA for its captain, according to Union manager Peter Nowak. The Union rejected an initial offer and the Goats then made a counteroffer that the Union is currently weighing.
Rumors of a potential move hit the blogosphere Saturday, and following Sunday's match, much of it was brought to light.
"Danny Califf's status is that we received an offer for him this last week and we informed the player right after it happened," Nowak said. "I talked to Danny . . . but we did not conclude anything, so as of right now he is still with us."
Califf missed his fifth match of the season against New York, because, according to Nowak, he is still hampered with injury issues from offseason knee surgery and a hamstring he strained last month. Califf missed a few practice sessions this week and was "not 100 percent ready for" the game against the Red Bulls, Nowak said.
Quakes, Goats draw. Alan Gordon a substitute in the 57th minute, headed in goal in the 89th minute salvaged a 1-1 tie for the San Jose Earthquakes against Chivas USA in Santa Clara, Calif.
San Jose (7-2-2) moved into sole possession of second place in the Western Conference, three points behind Real Salt Lake.
Marc Narducci: The Union are now 2-6-1 and not much has gone well, but this was by far their best offensive showing.
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This article contains information from the Associated Press.