The second-placed Swans trailed at every break in their AFL clash at Marvel Stadium on Saturday before mowing the Saints down 16.11 (107) to 13.10 (88), but their victory was overshadowed by Edwards' shocking injury.
The young backman was stretchered off midway through the final term after coming off worse for wear in a heavy collision, bleeding profusely from his head and - more concerningly - with his right ankle sticking out almost at right angles, delaying play for about 10 minutes.
Sydney were already one down with experienced midfielder James Rowbottom's afternoon finishing early with a suspected broken left hand.
"One of mixed emotions, to be honest," Cox said of his bittersweet feelings after the brave win which came on his 45th birthday.
"To see a player battle like (Edwards) already has for so long, to get a chance at AFL with some of the injuries he's already had, to dislocate his ankle and to be required to go to hospital and have surgery, it's devastating for him, the football club and his family."
St Kilda were also in the wars, losing full back Jack Silvagni late with a dislocated right shoulder.
Errol Gulden racked up 34 disposals and a goal for the Swans, while Logan McDonald booted four majors.
Charlie Curnow was blanketed for much of the day by Silvagni but finished with three goals, the last two coming after Silvagni's injury.
"They're never easy games against St Kilda," Cox said.
"They showed again that you've got to go right to the end to beat them."
Saints gun Nasiah Wanganeen-Milera shook off a hip concern from the Edwards collision to finish the match with 24 touches and three goals, while Max Hall also impressed with 23 disposals and three majors.
He was in everything early as the home side controlled proceedings to lead by nine points at quarter-time and 13 at halftime.
Turnovers were an issue for Sydney, who couldn't lay a glove on St Kilda on the outside.
Swans superstar Isaac Heeney had just seven touches at the half, tagged effectively by Hugh Boxshall.
Heeney goaled either side of the main break with a pair of one-on-one wins against Boxshall to close the gap to five points, before the Saints responded with the next three, highlighted by Wanganeen-Milera's classy snap out of congestion.
The Swans hit back and trimmed the deficit to 12 points when Gulden converted a free after the three-quarter-time siren.
From that point it was all Sydney, who won the final term 7.3 to 2.2.
McDonald jagged his fourth, Billy Cootee added another one, then Tom Papley put the Swans in front with a wonderful groundball gather and goal.
Heeney finally got off Boxshall's chain late, while fellow big guns Curnow and Chad Warner lifted in the crunch.
"We handled their ball movement out of the back half ... but stoppage they got us," St Kilda coach Ross Lyon said.
"(Playing) simply three quarters doesn't get it done."
