WATCH: Saturday Showreel - Luke Parker
Franklin was back in form in the Swans' 21.8 (134) to 9.17 (71) victory at Adelaide Oval.
Buddy booted four goals while teammate Harry Cunningham kicked three against the Crows, who remain winless after three games - and all defeats have been by heavy margins.
Crows 'leaning on the panic button': Sanderson
The Swans’ Parker was a standout and collected 26 possessions to form a dominant midfield combination with Josh Kennedy (28 disposals) and Jarrad McVeigh, who was also reported for rough conduct.
McVeigh collected Adelaide's Matthew Jaensch high in a first quarter controlled by the Swans, who skipped to a 6.2 to 2.2 lead at the first change.
Parker kicked two of his goals in the opening quarter and Franklin also scored to set the tone for his best performance in Swans colours.
Adelaide coach Brenton Sanderson admitted his team's 2014 season was almost in crisis already.
"We're not hitting the panic button yet but we're certainly starting to lean on it a little bit," he said.
Swans coach John Longmire was delighted with Franklin's game but emphasised his team's return to form was down to the 22 players who dominated the second-half.
"He (Franklin) played really well today but so did the other 21 [players].
"The guys made the change (in the third quarter) as far as laying some important tackles, winning some 50-50 balls. We thought our leaders were sensational when they were challenged."
Both clubs kicked three goals in an even second stanza but Adelaide lost club champion Scott Thompson, who was substituted in the 18th minute of the term with a corked thigh.
The Crows sorely missed his grunt around the packs and found themselves overly reliant on Richard Douglas (25 disposals) and co-captains Rory Sloane and Patrick Dangerfield (23 possessions) for midfield drive.
Adelaide, who fell 29 points behind early in the second term, launched a third-term comeback and crept to within two points midway through the third quarter.
And when Parker slotted his fourth major late in the quarter, the Swans established a defining 25-point advantage at three quarter-time.
McVeigh then booted the first major of the last term after a remarkable mark - the first of seven unanswered goals as Adelaide limply folded.
Lance Franklin had a day out for the Swans in Adelaide and his teammates couldn't have been happier. Picture: AFL Media
ADELAIDE 2.2 5.7 9.10 9.17 (71)
SYDNEY SWANS 6.2 9.2 14.5 21.8 (134)
Adelaide: Grigg 2, Mackay, Podsiadly, Dangerfield, Betts, Jaensch, Douglas, Sloane
Sydney Swans: Franklin 4, Parker 4, Cunningham 3, Hannebery 2, Jack 2, Rohan, Mitchell, McGlynn, Laidler, McVeigh, Roberts-Thomson
Adelaide: Podsiadly, Dangerfield, Douglas, Jaensch, Jacobs, Smith
Sydney Swans: Franklin, Parker, Kennedy, Jack, McGlynn, Malceski
Adelaide: Scott Thompson (corked thigh), Sam Kerridge (eye)
Sydney Swans: Nil
Adelaide: Scott Thompson replaced by Matt Crouch in the second quarter
Sydney Swans: Tom Mitchell replaced by Gary Rohan at three quarter-time
Sydney Swans: Jarrad McVeigh for rough conduct on Adelaide's Matthew Jaensch in the first quarter
Umpires: Margetts, Nicholls, Hosking
Official crowd: 47,426 at Adelaide Oval