Forwards Caitlin Foord and Hayley Raso scored the goals either side of halftime before Kerr, who has been absent with a calf injury, came on as a 78th-minute substitute to the biggest roar of the night from the crowd of 75,784.
Australia, who have reached the last eight at three previous World Cups but never gone further, move on to meet either France or Morocco in Brisbane on Saturday with a place in the semi-finals on the line.
"We were under a lot of pressure that first half but we didn't get rattled," said Australia coach Tony Gustavsson.
"The team is very mature playing tournament football and can find a way to get it done."
Denmark dominated the early exchanges with Pernille Harder looking particularly dangerous but faded as the game went on with their first World Cup campaign since 2007 destined to end in the last 16.
"The match today was decided by Australia's effectiveness in front of goal and our lack of efficiency in that area," said Denmark coach Lars Sondergaard.
"They probably deserved to win but I'm very proud of the Danish team. They fought hard, they played with heart."
The Danes looked far the better side in the first 20 minutes with their press disrupting Australia's attempts to build any fluency and Harder roaming up front probing for gaps in the home defence.
The Matildas forwards were being crowded out when they did make inroads into the Danish half and it was when their midfielders pushed forward from deeper positions that they looked most dangerous.
Fowler took the ball in such a position in the 29th minute and produced a stunning pass that carved through the Danish defence and found Foord streaking down the left channel.
Foord's touch took the ball to the edge of the six-yard box, where she slid it between the legs of Denmark goalkeeper Lene Christensen for her first goal of the tournament.
The pace of Foord down the left wing continued to cause problems for Denmark after the break and Emily van Egmond nearly turned her drilled pass across goal into the net in the 65th minute.
A huge roar went up four minutes later when Kerr was shown on the big screen putting on a match shirt but Australia had doubled their lead before she came on.
A Fowler pass into the box found Van Egmond with her back to goal and the midfielder controlled the ball well before sliding it out to Raso, who lashed it into the net from an angle.
Kerr's first touch was a wild crossfield pass to no-one but she was soon bursting into the box with the ball at her feet to fire a shot over the bar.
"It's massive for us to have a player like that back, it boosts our confidence," said Foord, who was named Player of the Match.
"We know we need to take it up another level if we're going to go all the way."
