The loss meant that the Wildcats finished the regular season in second spot and they will now turn their focus to a semifinal in RAC Arena on Thursday night.
The defending NBL champions entered the game severely undermanned following Norton joined superstar Bryce Cotton (leg operation ) on the sidelines.
Coach Trevor Gleeson stated Norton's unavailability arrived as a surprise.
We gave it a bit of rest and attempted to practice (on Thursday) but he couldn't practice," Gleeson said.
"He went for a MRI scan. Hopefully it is only going to be just one week and he will be back prepared for the play-offs however he certainly couldn't go tonight."
In a sign of how unsettled the Wildcats have been with injury, illness and roll changes going into the play-offs, Perth had their sixth different starting combination from the past ten games.
Playing in pink pajamas to raise money and awareness for Breast Cancer Care WA, the Wildcats scored only 29 points in the first half which was their lowest tally for the period.
They trailed by just four points during the final quarter before United retreated away.
Luke Travers continued his exciting end to the season with 10 points and eight rebounds, Will Magnay also scored 10 points while Todd Blanchfield top scored for Perth with 15 points.
The triumph locked away top place for Melbourne. Jo Lual-Acuil was superb with 16 points, Jock Landale scored 14 points along with Mitch McCarron gave Perth issues with 11 points, six rebounds and five assists.
Perth will sponsor Illawarra or even South East Melbourne from the semifinals. The Phoenix will move to third place if they win their remaining matches against New Zealand and Brisbane.
"We'll have a couple of days break and then return on Monday and lock into what we're doing for Thursday night," Gleeson said.
"We will only freshen the guys up emotionally too. I thought these games were fantastic for us. We had some adversity with Norto heading down and guys playing distinct roles out there. It is going to be a good lead-in for individuals to have two bodily play-off games prior to the play-offs actually begin. I am very happy about that.
"I just said to the guys in the locker room that I'm so proud of how we handled through the year.
"To finish second at 25-11 and 22 of those games were on the street, the adversity that we've gone through, and while we have not obtained the results in the last few games, we played with our hearts.
"If you'd told me in the start of the year that we'd be sitting next with 25 wins, I would have taken it straight away."