Grundy was involved in an absorbing ruck battle with ex-teammate Max Gawn as Sydney piled on four consecutive goals at the start of the final term to seal a 12.14 (86) to 9.10 (64) triumph in front of 40,012 fans at a sold-out SCG on Thursday night.
Isaac Heeney stepped up in a Swans midfield missing injured guns Callum Mills, Luke Parker and Taylor Adams, tallying 26 disposals, 18 contested possessions, one goal and a career-best 13 clearances.
Chad Warner (26 touches, one goal) and Nick Blakey (26 possessions) were also busy, while Hayden McLean and Will Hayward booted two goals each.
Hayden McLean kicks one of Sydney's 12 goals in the win over Melbourne. (Steven Markham/AAP PHOTOS)
Grundy, who left Melbourne for a third club during last year's trade period, finished with 22 disposals, nine clearances and 31 hitouts to edge Gawn in their duel.
He used his body well at ruck contests and left Gawn (15 disposals, two clearances, 39 hit-outs) nursing a sore hip late in the game.
Bayley Fritsch booted three goals in the third quarter to briefly give the visitors the lead - and finished with four - before they faded late in warm and slippery conditions.
Steven May was brilliant in defence but the Demons' scoring issues at the other end - a point of focus over summer - again reared their ugly head.
They managed just 2.8 from 29 forward entries in the first half.
Jack Viney (31 disposals, seven clearances, two goals) and Christian Salem (27 touches) fought hard against the tide for Melbourne and Clayton Oliver (29 disposals, six clearances) did well in his first senior game after a turbulent off-season.
It was a bruising contest, with Dees defender Jake Bowey sidelined after hurting right shoulder in collision with Justin McInerney not long after Jack Billings replaced Bailey Laurie as a tactical substitute during the third term.
Melbourne players paid tribute to recently retired teammate Angus Brayshaw before the match, taping up the much-loved utility's helmet in their change room and touching it on the way out onto the field.
Their inaccuracy was costly early as Oliver Florent booted the first goal of the season from outside 50m to help Sydney to a nine-point lead - 3.3 to 1.6 - at quarter time.
A dour second term featured just one major, from the boot of Swans forward McInerney, until Ed Langdon kicked truly with a set shot after the halftime siren.
Fritsch twice got the Demons back within a kick during the third quarter before putting them in front with a third major when most players stopped on an umpire's whistle and he took the advantage.
Melbourne kicked five goals to three for the term from just 11 inside-50s.
But the Swans turned for home two points in front and team-lifting goals from Warner, Will Hayward, substitute Sam Wicks and Robbie Fox gave the home side a match-winning buffer.
The run of four straight Sydney goals only came to an end in unusual circumstances when Jacob van Rooyen accidentally shinned the ball through as he fell over in a marking contest.
Sydney face another huge test when they meet reigning premiers Collingwood in a Friday night blockbuster next week, while Melbourne have 10 days until their home game against the Western Bulldogs.
