In front of 16,466 fans at HBF Park on Friday night, Kennedy struck in the ninth minute for her fifth goal of the tournament before Kerr made it 2-0 in the 47th minute.
World No.9 North Korea dominated for large parts of the match, and pulled a goal back in the 65th minute via Chae Un-Yong.
There were plenty of nervy moments from then on for Australia, with goalkeeper Mackenzie Arnold forced to make a series of diving saves, including one from a 38-yard effort from An Kuk-Hyang.
But the 2010 champions were able to hold on, setting up a semi-final against either China or Taiwan at Optus Stadium on Tuesday -- and the win also secured Australia the added delight of direct qualification for the 2027 World Cup in Brazil.
North Korea ended the match with 62 percent possession and fired off 21 shots to four in what was a dominant display -- but Australia had the two moments of brilliance that mattered the most.
"The most important thing today is the win," Kerr said.
"I thought it was a really good team performance defensively.Â
"They're a good side and they had a lot of the ball, and there was a lot of pressure at the end of both halves.
"But our mindset showed we came out both times and scored early, and that allowed us to go on and defend the game."
Australia unleashed just one shot in the first half - and luckily for the hosts it was a thing of beauty.
Kerr set up the goal after stripping her opponent of possession near the sideline and firing a cross into the box.
The ball deflected to Kennedy, who calmly took a touch with her right foot before firing in a thunderbolt off her left from the edge of the box to send the crowd into raptures.
The rest of the half belonged to North Korea, whose slick passing and pin-point crosses caused plenty of nervy moments.
Arnold had to dive to her left to save Kim Kyong-yong's header in the 26th minute, and the veteran goalkeeper was at it again seven minutes later when she blocked Chae Un-yong's angled strike.
The most nervous moment came in the final act of half-time when Hong Song OK's angled strike beat Arnold before hitting the upright and deflecting away.
North Korea enjoyed 58 percent possession in the first half and had fired in seven shots to one, with Australia struggling at times just to get the ball past halfway.
The half-time break did the world of wonders for the Matildas, with Kerr able to give the home side a 2-0 cushion after picking off an errant pass and nailing her left-footed strike from just inside the box.
Chae Un-Yong pulled one back for the visitors, but Mackenzie's strong work in between the posts ensured Australia held on.
Matildas substitute Clare Wheeler was left with blood streaming from near her right eye when she copped an elbow in the 84th minute, but she was able to play on.
Australia also have fitness concerns over Steph Catley and Hayley Raso after both missed the match with concussion.
