Replacing injured opener Aaron Finch, Head anchored a shaky Australian run chase with a polished 96, falling just shy of a deserved century and with victory imminent.
England were dismissed for 196 after being sent in to bat in bowler-friendly conditions, losing four of their top six batsmen for ducks as the possibility of a record low score in one-day cricket briefly loomed.
In reply, Australia reached the modest target with 13 overs to spare, finishing on 197 for seven, but the chase was not without concerns as they struggled to win their first game in the five-match series and turn around their dismal recent one-day form.
Australian captain Steve Smith admitted it wasn't the most convincing of wins.
"Nice to get over the line, a pretty ordinary (batting) display," he said, noting that the start to the English innings decided the match.
"It all happened pretty quickly for a moment there, five for eight you'd take any day."
England captain Eoin Morgan said his team fell victim to a lively pitch early.
Head looked certain to notch his second limited-overs century as Australia closed in on victory, but pulled a short ball from Mark Wood straight to Morgan at mid-on, having faced 107 balls and hit 15 fours.
That England were able to post any sort of competitive total was quite remarkable given their horror collapse in the early overs.
On Australia Day, it was all the home side as the tourists lost five wickets with just eight runs on the board.
Their lowest total of 86 looked in danger until all- rounder Chris Woakes came to the rescue.
In the end, solid resistance from Woakes (78) along with Morgan and Moeen Ali (33 each) -- and Tom Curran (35) -- enabled England to scramble to a decent total.
Woakes continued his excellent form with the bat in the series, hitting five sixes in the 82 balls he faced before being caught on the boundary off Andrew Tye (3-33).
The rot set in early for the tourists.
Alex Hales (3) was the second to fall, bowled off his pads by Pat Cummins, who snared a career-best 4-24.
Opener Jonny Bairstow was caught behind from the bowling of Hazlewood for a duck, and Test captain Joe Root also fell without scoring, caught on the fine leg boundary after top- edging a hook shot from the bowling of Cummins.
However, Woakes picked up where he left off in an unbeaten half-century in Sydney, and had good support from the previously out-of-form Ali and number 10 Curran.
The final match of the series is in Perth on Sunday, and is a sell-out as it is the opening of the city's new stadium.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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