Australia reached 317-3 with six overs to spare after bowling England out for 315 in 49.4 overs.
It was a 13th successive ODI win for last year’s World Cup winners, and sixth in a row over England, despite being forced to field a depleted line-up because of illness in their camp and injury.
Head’s highest ODI score, coming off 129 balls with 20 fours and five sixes, was ably supported by Labuschagne, who earlier had also proven key in restricting England’s strong start to the contest.
England, who won the toss and chose to bat, saw Ben Duckett fall five runs short of his century while Will Jacks scored 62 runs off 56 balls in a brisk start.
The pair put on 120 for the second wicket and even after Jacks' dismissal England were well set to go on and compile an imposing target as they reached 213-2 in the 33rd over.
But as a desperate Australia looked to stem the runs, having seen debutant quick Ben Dwarshuis forced off after bowling four overs having strained a chest muscle, they turned to part-timer Labuschagne, who put the brakes on the home team.
He dismissed Duckett with a slow leg break that sat up on the surface, deceiving the England opener who popped it up for an easy caught and bowled.
Labuschagne followed up his first ODI wicket in two years with two more, having England captain Harry Brook caught and bowled for 39, and going on to finish with figures of 3-39 in six overs.
Spinner Adam Zampa, who had been expensive in his first three overs, returned to take 3-49 as England lost their last eight wickets for 102 runs in 17 overs and were bowled out two balls shy of 50 overs as Head, the eighth bowler Australia used, took two-in-two in the final over.
Quick-fire
But it was still a healthy total, helped by a cameo from 20-year-old debutant Jacob Bethell, who contributed a quick-fire 35 runs.
Australia lost captain Mitchell Marsh early on in their reply and when Steve Smith went at 96-2 in the 16th over, they looked in potential trouble.
But Head kept battering the bowling and his unbeaten 148-run fourth-wicket partnership with Labuschagne saw the tourists comfortably home.
He did offer an early chance when he edged Jofra Archer wide of second slip when he had six runs but for the rest was imperious.
"I got a bit lucky at the start," said Head. "But if you could get through, there were a lot of runs on offer. It is nice I could contribute."
The second ODI between the two countries is at Headingley in Leeds on Saturday.