GWS trailed by one point at the final change, but kicked six goals to three in the final term to record a 16.6 (102) to 12.14 (86) win at Blacktown.
Both sides took turns in front in a closely contested game in which the lead changed several times.
While the youthful Giants invariably failed to run out games last year, that wasn't a problem in the sweltering conditions on Saturday.
Promising Giants' key forward Jeremy Cameron set the tone early with three goals in the first term which ended with GWS three points up.
They led by 10 at the long break, but St Kilda hit back to lead by a single point heading into the last term.
The industrious Giants midfield was sparked by Toby Greene with 32 possessions, Adam Treloar 28 and Stephen Coniglio with 25 each.
After watching his side suffer narrow losses to both NAB Cup finalists, Sheedy was delighted the Giants were able to win a close one and notch their second victory in five pre-season starts.
"We've got to get killer instinct into our game and slowly but surely we'll get that," Sheedy said.
"They fought it out and it was pleasing from that point of view.
"Our seconds had a really good win. We had five senior players that played pretty well in the reserves.
"So for the first time we will have pressure at selection and we've never had that."
Jack Steven excelled with 32 touches for the Saints, who suffered just their second loss in a series of pre-season games played in extreme heat.
"We've had four weeks where the best temperature we've had is about 30 degrees up to 39," Saints coach Scott Watters said.
"But I don't want to take anything away from what the Giants did today.
"I thought they ran harder, their contested ball was good and we were down in a few key areas."
Watters said he had been happy with a lot of things over the past five weeks.
"Some of the things that need tidying up will be tidied up on the back of work rate," Watters said.
"Just an inability today to work hard between the arcs. We were generally outnumbered at the contest whether the ball went forward or into our defensive half."