Phipps was a crucial part of the Tokyo Paralympics success and made vital contributions at the end of the first and second quarters as Britain started their Group B campaign in the sport nicknamed "murderball" strongly.
"It's an amazing start but nothing's happened yet," Phipps told AFP.
"Australia are a class act, we've battled with them for years.
"We still have to remember this is the start, so it's start as you mean to go on."
Phipps opened the scoring 15 seconds after the tip-off at the Champs de Mars arena, a venue in the shadows of the Eiffel Tower and which will also host para judo.
Britain led 14-13 at the end of the opening eight-minute quarter and held on to a one-point advantage with a 28-27 score at half-time.
With one quarter to play, they were 43-40 up after Phipps had scored his 21st try.
He then helped close out the win for Britain with his final try of the game with less than 30 seconds left.
Australia's Ryley Batt, a two-time Paralympic champion, scored 36 tries in a losing effort, while Phipps' team-mate Stuart Robinson had 23.
"It's unusual, it's normally Stu who scores the most," Phipps said.
"I'm usually the battering ram and Stu has the better hands.
"I'm usually the one to smash people about a bit."
Phipps, now 41, had his legs and most of his fingers amputated after contracting meningitis C as a teenager in 1999.
Eight years ago he became the first disabled British man to scale Mount Kilimanjaro and is now setting is eyes on back-to-back Paralympic titles.
"They're so different but I would love to take the two gold medals," Phipps said.
"Kilimanjaro was a crazy endurance thing.
"This is so intense, such a pressure cooker and you forget that until you get here."
Three-time former champions the USA start their Paralympics gold medal gold bid by facing Canada later on Thursday.
