Richards scored in the 67th minute with New York playing a man short, and the Red Bulls beat the Montreal Impact 2-1 to extend their Major League Soccer winning streak to five games.
The Jamaican striker pounced on a rebound off Montreal keeper Ricketts in close and put the ball under the crossbar to give New York its first lead.
"I was just in the box, lurking around, and the ball popped out to me and I just knocked it home," Richards said. "I know my countryman, Donovan Ricketts, he's unhappy with me right now but I had to do it."
Kenny Cooper scored his 10th goal to draw the Red Bulls even as both teams converted penalty kicks in the first half.
"It's a brilliant performance," Red Bulls coach Hans Backe said. "It's five in a row now with a quite inexperienced team. I mean, you can't demand anything else. It's almost shocking to pick up wins like that."
Bernardo Corradi scored his team-leading fourth goal 22 minutes in for the Impact, who ended a 2-0-2 run. Montreal lost at home for the first time in their last of five games at Olympic Stadium.
"It's frustrating because they basically come down the field one time," Impact coach Jesse Marsch said. "It's a play where we have a lot of numbers back and now it comes to the feet of Richards and he puts it in.
"It's an incredibly disappointing and frustrating game because we just let this one slip away, but in a lot of ways our ideas and our attempts were not bad."
Cooper tied it 1-1 when he drove a shot into the top right corner 37 minutes in as New York benefited from a hand ball by Impact defender Tyson Wahl.
The Red Bulls striker moved past injured teammate Thierry Henry for the team lead in goals. Cooper is now second overall in the MLS behind only San Jose's Chris Wondolowski.
Montreal fell to 0-2 against the Red Bulls. Henry scored a hat trick in New York's 5-2 win on March 31.
"I certainly think that this one hurts just as much but this one hurts to be at home, and especially being a man up," Impact defender Jeb Brovsky said. "Knowing that we had the lead and giving that away, it really hurts us. We're not happy about it but we know that we're going to look at film and just keep learning."
A crowd of 20,373 was on hand one week after a Canadian professional soccer record 60,860 came out for a 1-1 tie against David Beckham and the Los Angeles Galaxy.
The Impact's next home game is June 16 against Seattle at adjacent Saputo Stadium, which has been renovated to expand its seating capacity from 13,034 to 20,341.
Richard Legendre, the executive VP of the Impact and Saputo Stadium, said that the team had a goal of drawing an average crowd of 35,000 for the five-game stint at the domed home of the 1976 Olympics. Montreal's total home attendance at the Big O was 182,488, a five-game average of just under 36,500.
"We are very, very happy," Legendre said. "Olympic Stadium served us well."
New York was down to 10 men in the 58th minute after Victor Palsson was shown his second yellow card of the match. Referee Ismail Elfath brought out the red card after Palsson was called for a trip from behind on Impact striker Miguel Montano. Palsson earned his first yellow card four minutes in for his hard tackle on Felipe.
Montano, who made his first start, hit a long drive that struck the left post in the 63rd minute. He also put a shot wide of the left post from the right side shortly after Palsson was sent off.
"He was close to making a couple of plays tonight," Marsch said. "In training a lot lately he'd shown that those kind of plays have gone in for him and that's why he now was on the field. It didn't go in for him tonight but I think he'll find more chances this season and get some goals."
Ricketts made a lunging catch two minutes into the second half, diving to his left to snare Red Bulls midfielder Joel Lindpere's left-footed drive towards the top right corner.
The Montreal goalkeeper fared worse on New York's go-ahead goal. Ricketts deflected Roy Miller's centring feed from the left side of the goal-line in front, and Richards made no mistake with his shot at the gaping upper part of the goal.
Corradi gave the Impact a 1-0 lead when he drove his penalty kick past Red Bulls 'keeper Ryan Meara into the left side of the net. Montreal was awarded the penalty kick after Corradi was hauled down by New York captain Markus Holgersson.
Heath Pearce played 90 minutes in his Red Bulls debut. The American defender was acquired from Chivas USA on Thursday in a trade for Juan Agudelo.
"A different class," Backe said. "I've seen him so many times in Denmark and Germany and he's so composed. He has everything."