After seven lead changes in a see-sawing first quarter, Rosas slotted five goals before halftime to help set up a 19.17 (131) to 17.12 (114) victory at the SCG on Saturday.
The Demons slammed through four-straight goals in the final quarter to send a scare through the Swans camp, but Joel Amartey kicked his fourth goal late on to seal the deal.
Moving to the Harbour City this year after six seasons at Gold Coast, the 24-year-old Rosas became only the fifth Swans player in the past 10 years to kick seven or more goals in a game.
The joint ladder-leading Swans improved their record to 6-1, with Logan McDonald kicking three goals as former Demons ruck Brodie Grundy marked his 250th game in fine style in front of 40,673 fans.
Melbourne were gallant but hit another speed bump in their first season under coach Steven King, dropping from fourth to sixth (5-2).
"It's an interesting one, really disappointed with the result today, but really proud of the group for fighting it out," King said.
"Although we don't walk away with four points, I walk away really proud as a coach, knowing I've got a group of players that are willing to fight and scrap to the death and never give in."
A hamstring injury to key forward Brody Mihocek only added to Melbourne's woes after a week of off-field turmoil.
The Demons are preparing for a legal battle with former chief executive Paul Guerra, who was sensationally axed on Tuesday in favour of Daniel Taylor.
Melbourne's leading goalkicker with 13 goals so far, Mihocek lasted less than four minutes on Saturday after straining his left hamstring in a contest with Swans defender Lewis Melican.Â
Mihocek's absence meant captain Max Gawn was moved deeper into attack, and youngster Max Heath was tasked with an in-form Grundy.
Heath tried earnestly but Grundy (one goal, 10 clearances, 45 hit-outs) easily shone in his milestone match.
Justin McInerney (one goal, 29 disposals, five clearances) was just as crucial and ran rampant alongside Nick Blakey and Isaac Heeney, on return from a calf injury.
While "not rapt" with the final quarter, Swans coach Dean Cox heaped praise on his firing forward line led by high-profile recruit Charlie Curnow.
"That's my number one focus, (which) isn't to rely on one person," Cox said.
"Melbourne really defended the corridor well, so we had to go around them and find a different avenue.
"We want to make sure that we can collectively kick a score."
Rosas slotted two goals in the opening quarter before Demons youngster Harry Sharp matched the feat to help the visitors hold on to a two-point lead at the first break.
But Melbourne couldn't build on their momentum, with Rosas kicking three more goals as the Swans broke out to a 22-point advantage by halftime.
Sydney could only grow their margin by three points in the third term, before proven Demons match-winner Kysaiah Pickett kicked the first of four majors in the final quarter.
Amartey killed off the challenge when the Demons gave away a costly 50 metre penalty.
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