Brisbane's superiority was measured by the fact they had a total of 17 shots on goal, nine from inside the box, and made 26 incursions into Sydney's penalty box in the first while Sydney made only one into Brisbane's.
Smith scored Brisbane's first goal with a glancing header from a Broich free kick. Their second came only a minute later when Ivan Franjic headed on a corner to the unmarked Henrique who finished from close range.
North broke a five-year scoring drought with the third goal which ensured Brisbane continued an eight-match winning streak over Sydney in Brisbane.
"I thought we were frustrating them up until the two set-piece goals and after that there was only one team," Farina said. "The Roar are a side you can't give 2-0 leads to and then expect it to get any easier.
"They were very good, I have to give them credit. They are a very, very good team and we were nowhere near our best. It was a good wake-up call for our players."
Marcos Flores scored twice from the penalty spot as champions Central Coast rallied from 2-0 down to snatch a 2-2 draw with the Melbourne Heart.
David Williams netted twice for Melbourne, tapping home the rebound of Golgol Mebrahtu's deflected shot in the 54th minute then scoring off Iain Ramsay's centering pass six minutes later.
But Flores leveled the score with penalties in the 71st and 73rd minutes, the first for a foul by Patrick Kisnorbo on Matt Simon and the second after the ball struck the hand of substitute Frank Gerhardt.
Ange Postecoglou, tipped as Australia's next national coach, saw his Melbourne Victory team score twice in the last 15 minutes to snatch a 2-2 away draw with Adelaide. Sergio Cirio, from a contentious penalty, and Jeronimo Neumann gave Adelaide a 2-0 lead but the Victory rallied with goals to Guilherme Finkler in the 79th and James Troisi three minutes from fulltime.
On Sunday Newcastle and Perth drew 0-0 and Wellington came from behind to grab a 1-1 draw with Western Sydney.