One team played the New York Derby as if it were just another game. The other played it as if it were the only game.

Guess which one won at Red Bull Arena.

Expansion New York City FC spent all week downplaying their first clash with the Red Bulls The hosts openly talked about having to win for their supporters, about needing to beat their rivals no matter what. And they backed that up.

The short-handed Red Bulls beat NYCFC 2-1, and it could have been worse. They played nearly two-thirds of the game a man down, but had more energy and urgency before a raucous sellout crowd of 25,217 — including 1,500 blue-clad ones that left sullen.

“It showed what it meant to a lot of us,’’ Red Bulls captain Dax McCarty said. “We tried to downplay the rivalry aspect of it, but whenever a team comes and brings 2,000 fans and they’re loud and we hear them, you always want to win, and you always want to shut them up.’’

They shut the road fans up quickly, Bradley Wright-Phillips scoring in the fourth minute and again in the 52nd. Even after Patrick Mullins pulled a goal back in the 76th minute, the Red Bulls (4-1-4, 16 points) closed the game out despite playing with 10 men from the 36th minute on.

“They came out with more energy than us,’’ said NYCFC defender Chris Wingert.

“Maybe not enough urgency,’’ midfielder Ned Grabavoy conceded.

Before the game, NYCFC coach Jason Kreis said he hadn’t noticed any extra hype and Jason Hernandez called it just another game. But after Hernandez got beat for Wright-Phillips’ first goal, it was obvious to whom this game meant more.

The Red Bulls went around clapping to their supporters and NYCFC went back across the Hudson winless in eight straight with a laundry list of things to figure out.

“Unfortunately we’re in a bad situation and a bad run,” NYCFC star David Villa said. “We’re in a bad spell. We’ve hit rock bottom and we need to continue to work hard. It definitely hurts. We need to regain that confidence and turn this around.’’

Despite Matt Miazga getting sent off for a second yellow card, the Red Bulls looked more composed than a high-priced NYCFC team that’s 1-6-3, with MLS’ worst goal differential. It can’t be the return on investment Sheikh Mansour bin Zayed al Nahyan expected.

Frank Lampard still hasn’t shown up yet, and Villa started his first game since April 16. But the $6 million man didn’t finish it; Kreis pulled Mix Diskerud in the 64th minute and Villa four minutes later, the latter twice looking at Kreis incredulously, turning his arms up and muttering.

“David was a little frustrated on the night, coming back from an injury and has a little bit of rust he needs to knock off,” Kreis said. “At the end of the day we have to make decisions that are a bit more future-thinking than just trying to get a result.’’ said Kreis, who pulled Diskerud less for precaution but more for his play.

“I thought Mix was just not great. … He was in and around things and not making plays either in the attacking half or the defensive half.’’

Diskerud was not made available to the media and wasn’t visible after the game, much as he had been invisible during the game with U.S. coach Jurgen Klinsmann watching from the stands.

“We have a lot to learn from this,’’ Mullins said, “not just move on past it but take the things and learn.’’

One is: Respect your rivalry.