Speedy debutante Murphy, one of nine changes from the last-start heavy loss to Canada in June, received a long pass from fullback Samantha Treherne 25m from the line, slicing through defenders to score untouched.
Treherne missed the conversion, helping Ireland to a 7-5 lead in half-time.
The visitors took a three-point lead when co-captain Shannon Parry drove over in the 56th minute, with Treherne again failing to add the extras.
But world No.5 Ireland, who dominated the match for territory and possession, hit back with two tries to lead 19-10 with nine minutes remaining.
Wallaroos substitute Ashleigh Hewson scored in the 73rd to set up a tense finale.
But the hosts held on for a perfect start to their campaign as Stapleton’s boot proved decisive, slotting two from three conversions.
Wallaroos coach Paul Verrell said his world No.6 side had improved from their winless Four Nations tour of New Zealand two months ago.
“The team matched it with the Irish and for the majority of the match and matched them in physically and put in a solid defensive display,” Verrell said.
“The Irish controlled possession for a large portion of the second half and kept the ball inside our own half and that prevented us from creating any real opportunities.”
Australia will begin preparations for their August 14 clash with France, who lead the group after a a 72-14 win over Japan.
Canada beat Hong Kong 98-0, while New Zealand fullback Selica Winiata bagged a hat-trick to help the four-time champions overrun Wales 44-12 in pool A
In pool B, England beat Spain 56-5 and the United States defeated Italy 24-12.
The Wallaroos will look to take something out of the 2019 Laura O’Reilly Trophy when they take on the Black Ferns in Game 2 of their series at Eden Park. This is The Roar’s guide to streaming the match online, or watching it on TV. While the first game of the series was played in […]