The Demons conceded six of the first seven goals and were always playing catch-up, eventually slumping to a 14.7 (91) to 7.21 (63) defeat in Alice Springs on Sunday.
They were convincing winners in the territory battle - leading the inside-50 count 57-40 - but were woefully inaccurate in front of goal.
Melbourne kicked 5.19 after quarter-time, including 0.8 in the final term.
It left the Demons' win-loss record at 5-7, level with St Kilda, before a King's Birthday blockbuster against flag favourites Collingwood.
"It's frustrating," Melbourne coach Goodwin said.
"If you want to make a difference to how the game looks you've got to get scoreboard impact.
"When that happens you'll change the way the game's being played, but we weren't able to maximise our opportunities, especially after quarter-time."
After jumping out to an early lead, St Kilda were able to get numbers behind the ball and hurt Melbourne on the break.
"Early in the game, what I was most disappointed with was our ability to win contest and defend the ground," Goodwin said.
"There were way too many full-ground transition goals.
"The way we started set the game up the way St Kilda wanted it and we weren't able to get the scoreboard impact to change it."
St Kilda small forward Dan Butler shone with four goals in his first game of the season after overcoming an achilles issue.
Isaac Keeler added three goals and Nasaiah Wanganeen-Milera (29 disposals) was influential after passing a concussion test following a high bump from Demons forward Aidan Johnson.
Johnson, a mature-age draftee, has already been suspended this season and faces further scrutiny for his latest indiscretion.
Jack Sinclair (25), Callum Wilkie (31) and captain Jack Steele (23) also had a say for the Saints, while Marcus Windhager (28 touches) and Zak Jones (20) got busy while keeping tabs on Melbourne stars Kysaiah Pickett (12) and Clayton Oliver (16) respectively.
St Kilda's second win in eight weeks snapped a three-match losing streak.
"We've been really working hard on our football," Saints coach Ross Lyon said.
"It's easy to talk about but we worked hard on it and I thought we executed today.
"We were a bit harder today in the centre-square bounces, where they're really strong, and we stood up in that area of the ground.
"That really helped us, so I was pleased."
St Kilda lost Mattaes Phillipou to a calf injury in the first quarter, but Lyon said the young gun should be fit to play immediately after the mid-season bye.
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