Earlier, Australian opener Aaron Finch had scored his ninth one-day worldwide century to leave England chasing a target of 305.
In Test cricket, however, England have stumbled, losing 18 of 38 Test matches under Bayliss including the recent 4-0 Ashes defeat. This is also England's first win of the tour after a dismal Ashes performance.
Joe Root (91 not out) played a fine supporting role in a mammoth third-wicket partnership of 221 as England pulled off the highest ODI chase in Melbourne easily, comfortably overhauling their opponents' total of 8/304 with seven balls to spare.
In addition to surpassing Alex Hales' benchmark of 171, made against Pakistan 17 months earlier, Roy also set a new record for the most substantial innings at the MCG, going past Mark Waugh's 173 for Australia against West Indies in 2001.
Yep, we're into the One Day Internationals!
"It is extremely special, especially after our Test series", added Roy. In fact, between them they have played just 34 List A matches - Tye 24 and Richardson eight.
Marcus Stoinis gave the hosts some late impetus with a rapid 60, but Roy began to reclaim the momentum for his side with some dashing strokeplay to kick-off the chase.
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Even though captain Eoin Morgan and wicketkeeper Jos Buttler fell shortly after, England reached their target with seven balls to spare thank to Root's unbeaten 91, which came off 110 balls and included five boundaries. It was a tough season last season so to be selected this time was incredibly special.
City finally stumbled at a ground where the team has a long history of struggles - with just one league win in 37 years - and was ultimately undone by nine minutes of madness around the hour mark when Liverpool scored three goals.
In 148 ODIs at the MCG, this is the first time a side has scored more than 300 batting second. "It sums up the character of the bloke, coming back in".
"Yeah too right, a bit of their own medicine was quite nice", Roy said when asked about whether it had been helpful to see Austrlaia's batsmen discomforted by speed. He chanced his arm and it came off and he was supported really well by Joe Root.
"We probably left ourselves a few short, we lost a few wickets in the middle and that stopped us going from as hard as we liked at the back end", Smith said at the post-match presentation.
"We got a huge amount of confidence from the selectors and Andrew Strauss, our director of cricket, gave absolute clarity in what we wanted". We have done that a bit with the bat, we will try and continue taking wickets with the ball.