Off the back of a five-day break and missing four key players, Collingwood made the most of their limited forward 50m entries to post the 15.7 (97) to 12.11 (83) win in front of 47,780 fans on Thursday night.
Elliott was the star of the show with 6.2 from 14 disposals, while Jack Crisp tallied 29 disposals, six clearances, 718m gained and one goal just a week after missing his after-the-siren shot in a three-point loss to Geelong.
Fremantle won the clearances 44-29 and the forward 50m count a whopping 63-34 in what was a much-improved showing from last week's listless 61-point loss to St Kilda.
But the Dockers' haphazard entries cost them dearly, with Collingwood's defence able to pick off the ball time and again in a masterclass display of counter-attack football.
It left Fremantle nursing a 4-5 record and needing to answer all sorts of questions about why their talent-laden squad can't get the job done, even when they dominate the stats.
In a further blow, injury-prone ruckman Sean Darcy was subbed out during the third quarter with a jarred knee.
It was a brave win for Collingwood, who were able to improve their season record to 7-2 despite being without Brody Mihocek, Scott Pendlebury, Jordan De Goey and Brayden Maynard for Thursday's match.
Star midfielder Nick Daicos tallied just 18 disposals, four clearances and a goal while batting a hip-back issue, while Lachie Schultz was heavily concussed early in the final quarter, just minutes after Steele Sidebottom was subbed out.
Schultz was knocked out after copping a shoulder to the head while laying a tackle on Jordan Clark.
"We're really, really ecstatic with that win. That's a huge performance," Collingwood coach Craig McRae said.
"To come over here off a five days (break) and a travel is hard to do.
"We didn't want to under understate or overstate it before the game, but we knew it was going to be a big challenge.
"We give a massive shout-out to Jarrod Wade and our high performance team."
Clark (33 disposals) played a pivotal role in defence for Fremantle, while Andrew Brayshaw (33 disposals, six clearances) was busy in the midfield.
Fremantle enjoyed a dream start to the match.
Josh Treacy, who was held scoreless last week, kicked the first two goals of the contest, and it was 21-1 when Isaiah Dudley joined in on the fun.
The Magpies kicked the final four goals of the quarter to take a five-point lead into quarter time, with Schultz's desperate pressure without the ball leading to two of those majors.
Fremantle captain Alex Pearce marked the upcoming one-year anniversary of Cam McCarthy's death by kicking a long-range goal to start the second quarter.
Pearce paid tribute to his good mate by kissing the word Dardy - McCarthy's nickname - which was written on his tape.
Collingwood's ability to get out the back to score goals on the counter continued in the third quarter.
Two goals to Bobby Hill helped extend the margin to 21 points before Pat Voss pegged one back, and three goals to Elliott in the last quarter gave Collingwood the breathing space they needed.
"The difference in the game clearly was their efficiency inside 50 and our inefficiency going forward," Fremantle coach Justin Longmuir said.
"To kick 83 points from over 60 inside 50s - we need more bang for buck.
"We fell into bombing the ball in there probably a little bit too much. And at stages we were just unpredictable with those long kicks."
