"Big win for us," Hardy said.
Cruz and Pearce each had a two-run shot. Hardy ended a drought of 339 at-bats that dated to last September.
"It definitely felt nice," he said. "I felt like I forgot how to do it."
"I think it probably is a little bit of a relief. I started to question myself if I ever was going to hit one again," Hardy added.
Mark Teixeira hit his 12th home run for the Yankees, who had won four straight and eight of 10, but that was all they managed against Norris and three relievers.
During a pregame ceremony on the field, former New York first baseman Tino Martinez was honored with a plaque to be placed in Monument Park.
Making his first start against the Yankees, Norris (7-5) allowed three hits in five innings and matched a career high by winning his fourth straight start. He warmed up on the mound for the sixth but was pulled for Ryan Webb, who pitched two scoreless innings.
Tommy Hunter got the final five outs.
Norris said he felt something "kind of funny" while throwing a fastball in the fifth.
"It kind of grabbed on me," he said. "I've had groin stuff before, especially my left one but not necessarily my right one. You've got to be real careful with those."
"I could see it getting a little worse and I wanted to be smart, but really, hats off to the offense for scoring and to the bullpen for picking me up," Norris added. "Pretty sore right now."
Orioles manager Buck Showalter said Norris probably will pitch the night game of a split doubleheader Friday against Tampa Bay, but the right-hander said it was too soon to tell.
"We've got other options, but I'm hoping we caught it in time," Showalter said.
Pressed into the rotation because of injuries to CC Sabathia, Ivan Nova and Michael Pineda, Nuno (1-4) is having a hard time with the homer-friendly dimensions at Yankee Stadium. He was rocked in his previous outing in Oakland and is 0-4 since beating the Los Angeles Angels on May 7.
"This is what we have. And as I said, it's not like there's just starting pitchers lying around out there," New York manager Joe Girardi said, explaining that Nuno will stay in the rotation. "Right now, this is what it is."
The left-hander yielded five runs -- four earned -- and six hits in 6 1/3 innings. He allowed three home runs and has served up 13 in 39 1/3 innings this season at home, where he is 0-3 with a 7.09 ERA.
"My fastball today, I just left it up too much," Nuno said. "I trusted all my stuff today. No regrets and everything, but they just got to my fastball."
Jones hit a solo shot with two outs in the first and drew a leadoff walk in the fourth before Cruz connected. Cruz began the day one home run behind Toronto slugger Edwin Encarnacion for the major league lead.
"He's carried us along a lot of the season," Hardy said.
"We like hitting home runs," Jones said.
Back in the dugout, Hardy got the silent treatment. He threw sunflower seeds on himself and was doused with water by Cruz.
The two-time All-Star shortstop has hit at least 22 home runs five times, including a career-high 30 with Baltimore in 2011.
"Normally I just put my head down and run. This time I kind of watched a little bit to make sure that it got up," Hardy said. "As I was rounding third, I looked into the dugout and no one had moved. So I kind of knew that they were going to sit there."
Baltimore recalled reliever Brad Brach from Triple-A Norfolk. ... Nuno has allowed 15 homers in 67 1/3 innings overall. ... Pineda (right shoulder muscle) will get another week off after an MRI still showed "a trace of inflammation," Girardi said. ... RHP Masahiro Tanaka (11-1, 1.99 ERA) starts Sunday's series finale against Orioles RHP Chris Tillman (5-4, 4.82). Hall of Fame reliever Rich "Goose" Gossage will be honored with a Monument Park plaque as part of festivities for the 68th annual Old-Timers' Day at Yankee Stadium.