NEW YORK >> A border collie named Trick rocketed to a win full of four-footed focus in the Westminster Kennel Club dog show agility contest today. And next door, also tackling hurdles, tunnels and weaving poles, were some decidedly rare breeds for the Westminster world:

Cats.

For the first time, felines sidled up to the nation’s premier dog show, as part of an informational companion event showcasing various breeds of both species. It included a cat agility demonstration contest, while more than 300 of the nation’s top agility dogs vied in a more formal competition.

Trick topped a field of 50 finalists to take the agility title with her owner and handler, John Nys of Pascoag, Rhode Island. Intensely athletic and willing, “she really is a team player,” he said.

A former shelter dog named Crush won a separate title for the top mixed-breed dog in the competition. Not “a sit-on-the-couch-dog,” Crush needed activities to focus on, says owner and handler Aryn Hervel of American Canyon, California. Besides agility, Crush works sniffing for sewage leaks, Hervel said.

While there weren’t exactly cats in the 140-year-old dog show, their inclusion in the “Meet the Breeds” event came close enough to prompt some “what?!” and waggish alarm about a breakdown in the animal social order. Some Twitter users have portrayed the development as a sign of impending cat-astrophe. A satirical Chicago Tribune column declared that “we can’t just let cats start racing across the borders of traditional dog events.”

Even some Westminster competitors found the juxtaposition jarring — or “so weird,” in the words of Hannah Naiburg of Milford, Connecticut, who guided her terrier mix, Molly, to the final round of Westminster’s agility contest. But others tipped their hats to the cats that were padding and prowling around their own course, most of them trying the sport for the first time.

“Good for them,” said Tina Ackerman of New Hampshire, who handled her bichon frise, Bubba Watson. “There’s no way we could ever have trained any of our cats to do agility.”

Bemisu, a 1-year-old sphynx cat nicknamed Misha, had never tried the sport before Saturday. But within a half-hour, she was following owner Blake Gipson’s toy-dangling signals to hop through hoops and run through a mesh tunnel — so well that she bested about 30 other cats to win.

“I had no idea she would learn so fast,” said Gipson, whose nearly hairless, down-covered cats share his Denver home with a pit bull. “She’s smarter than I ever gave her credit for.”

If today’s “Meet the Breeds” event — sponsored by Westminster, the American Kennel Club and The International Cat Association — gave felines their first chance to share Westminster’s spotlight, it also illustrated that there’s plenty of everyday crossover between the dog and cat camps. In fact, a 2011 CBS News poll found that 23 percent of American pet owners have both a dog and a cat.

Agility is increasingly popular for both species, seen as a way to give the animals activity and strengthen the bond between pets and their people.

Lonnie, a mixed-breed dog born in an animal shelter, used to be “afraid of everything,” even being in a car, owner Robin Lembo said. She started training Lonnie in obedience and then agility to build her confidence. Now, the 8-year-old dog is so outgoing that she eagerly ran the agility course in front of crowds Saturday.

And Lembo is all for cats getting into the agility act.

“I keep telling my husband to try it — because he’s a cat lover,” said Lembo, of New Jersey.

As every cat owner who has watched his pet walk along a railing knows, feats of agility come naturally to many felines. But training? A cat?

It’s easier than many people think, though cats are often more motivated by chasing toys than getting treats, said Vickie Shields, who oversaw Saturday’s agility demonstrations. A former trainer of dogs for field trials, she helped organize cat agility as a sport in 2003, largely with the goal of getting people to play more with their cats.

“People think cats are solitary. They aren’t,” said Shields, of New Mexico, noting that wild cats often form colonies. “You can do stuff with them, too. It’s not just dogs.”