Edwards: Glory win over Heart 'crucial'
But Glory now sit mid-table with four points from the opening three rounds and have another home match against Sydney FC next Saturday.
Before a crowd of 13,856 in their first home appearance of 2013, Perth dominated the first half but failed to capitalise before Jamie Maclaren struck five minutes after the break with what proved to be the winner.
Edwards said he felt Perth deserved the three points, despite their wastefulness in front of goal.
"The way the league is going it's very competitive and it's very hard for teams to win away from home," he said.
"For us to get the home win and send our great fans home happy it's an important first-up game at NIB.
"It would have been good to get a few more goals, hitting the woodwork a few times, but on the whole, very good."
Heart were without Harry Kewell as he recovers from a whiplash injury sustained in Round 1, and head coach John Aloisi said he is not sure whether the captain would be available to face Brisbane Roar next weekend.
"We have to see how he is day-by-day and see if he can get up," Aloisi said.
"We'd love for him to be available because he's an important player for us.
"At the moment we're putting David Williams in there, he's not really a number 10, even though he did well last week, this week he didn't get on the ball as much and when he went back out wide he got in good areas and started causing problems.
"We'll wait and see how Harry goes and make a judgement on that later in the week."