It's a much needed confidence boost for the visitors, who haven't notched up a win against an Australian team since their tour match against an invitational side the week before the Ashes commenced.
But their score of 8-264 off 50 overs once again came primarily from the middle order, with Cook and first drop Joe Root both falling cheaply.
After winning the toss and electing to bat, England got off to a shaky start thanks to a fierce opening spell from PM's XI captain Brett Lee (2-22 from seven overs).
Cook (1) was caught behind on his second ball when Lee got one to rise quickly just short of a length.
It means the England captain has averaged just 20.91 in his last 12 innings on Australian soil.
Root didn't look any more confident at the crease, notching up one run from 14 deliveries when Lee trapped him lbw.
But England's early innings troubles proved to be nothing compared to the PM's XI team, whose top five order batsmen managed to scrape just 51 runs between them - Brad Hodge (28) offering up the only resistance - before being bowled all out for 92.
Ravi Bopara (4-3 from three overs) and Boyd Rankin (2-39 from eight overs) were the pick of the English bowlers.
As opposed to their hosts, the England side managed to overcome their early troubles, Michael Carberry (47), Gary Ballance (56), Jos Buttler (61) and Tim Bresnan (36) all chipping in with handy innings.
The one silver lining for the PM's XI was the performance of 20-year-old legspinner James Muirhead (3-52), who dismissed batsmen Ballance, Eoin Morgan (4) and Ravi Bopara (18).
The 20-year-old Victorian had the English batsmen in all sorts when he got his length right - but also gave away plenty of runs with long hops and full tosses.