Both sides enjoyed periods of momentum in a scrappy game before Sydney finally broke it open in the second half, kicking seven-straight goals either side of the last break to set up a 16.7 (103) to 12.15 (87) win.
In one final shift, GWS slashed a 33-point deficit to 10 with four-consecutive goals, before Franklin soothed the nerves of Swans supporters and ended the Giants’ charge.
The previously scoreless forward settled the issue with a booming kick of almost 60 metres.
Will Hayward goaled again soon after and Franklin closed the show with a second major to add to his 22 possessions and 10 marks.
Callum Sinclair kicked three goals for Sydney, while Franklin, Hayward, Tom Papley, Gary Rohan and Sam Reid all finished with two.
Sydney’s Callum Mills won the Brett Kirk Medal for best on ground, tallying 26 possessions. For the Giants, Nick Haynes finished with 28 and Stephen Coniglio 27.
The result leaves both sides with a 2-1 record and the Giants have still to win their first three matches of a season.
GWS enjoyed a 47-33 advantage in clearances, but were often guilty of poor kicks into their attacking 50 and wayward kicking when they did have scoring opportunities.
Sydney kicked three unanswered goals to lead 22-11 in the first quarter, before Matt de Boer broke the streak from a free-kick just before the break to cut the Swans’ lead to five points at the first break.
GWS carried that momentum into the second quarter and hit the front with with successive majors from Stephen Coniglio and de Boer.
The tide turned again, with the Swans kicking the next four to lead by 13, with Sam Reid converting a couple of strong marks into set-shot goals.
Jeremy Cameron, who led the Giants’ goalkickers with three, kicked an opportunistic major after a Swans error, as GWS pulled back to within six points at halftime.
Continuing the trend, GWS booted the first two goals of the second half through Cameron and Rory Lobb to reclaim the lead.
But Sydney followed the script of the night and added a bit of additional scoreboard impact before withstanding the last Giants charge.
The Giants’ de Boer was reported for rough conduct on Sydney’s Lewis Melican.
© AAP 2018
SYDNEY 3.4 7.4 12.5 16.7 (103)
GREATER WESTERN SYDNEY 2.5 5.10 7.13 12.15 (87)
Goals: Sydney: C Sinclair 3 G Rohan 2 L Franklin 2 S Reid 2 T Papley 2 W Hayward 2 I Heeney J Kennedy L Parker. Greater Western Sydney: J Cameron 3 D Lloyd 2 M De Boer 2 H Himmelberg J Hopper J Patton R Lobb S Coniglio.
Umpires: Troy Pannell, Ray Chamberlain, Robert O’Gorman.
Official Crowd: 34,711 at SCG.