Leading by 28 points 12 minutes into the final term, the Dockers' advantage was almost wiped out as the Bulldogs slammed through the next four goals.
But star Fremantle ruckman Luke Jackson's desperate tackle on Bontempelli with two minutes left created a passage of play that allowed Shai Bolton to snap the match-winning goal.
The Dockers met the Bulldogs' final challenge to win 17.12 (114) to 15.12 (102) for their seventh-straight victory - their best winning streak since they won the minor premiership in 2015.
Receiving a quarter-time spray from coach Justin Longmuir when they were 26 points down, the Dockers rallied as the Bulldogs wilted.
Two stunning goals from Hayden Young late in the third quarter helped Fremantle hit the lead for the first time just before the final break.
Young then slotted a goal of the year contender early in the final quarter as Fremantle's midfield momentum seemed irresistible.
It was the classy left-footer's 13th game in the last two seasons, having been cut down by hamstring injuries.
"We're probably in that stage now where we don't have to rely on one or two, and then sometimes it's one player bobbing up and having their moments," Dockers coach Justin Longmuir said.
"We're sharing a load the well, but he got some looks and finished off his work.
"When he gets on a tear like that you see what he is able to do."
The Dockers banged through six-straight goals either side of three-quarter time.
Fremantle appeared home when Andrew Brayshaw snapped truly to put them 28 points in front, accidentally whacking teammate Josh Treacy in the eye during celebrations of the goal.
But Bontempelli, who finished with a game-high 33 disposals and booted two goals, threatened to rain on the purple parade, despite struggling with a knee issue for the last three weeks.
Fremantle's midfield was exposed in the first quarter, as Bontempelli, Ed Richards and returning ruck Tim English caused chaos.
But Jackson, Bolton (30 possessions, nine clearances) and Brayshaw lifted to engineer the Dockers' resurgence.
Already with seven first-choice players on their injury list, fringe forward Laitham Vandermeer suffered a hamstring strain in his first AFL appearance of the season.
After starting the season with four-straight wins, including beating reigning premiers Brisbane at the Gabba, the Bulldogs have now lost four matches in a row.
"Regardless of who's in or out of the team, our purpose is to instill belief in the 23 that play," Bulldogs coach Luke Beveridge said.
"I stand in front of them and talk to them, and they know I really believe it.Â
"They know I believe in them and there's no other way to be."
In better news for the Bulldogs, star forward Aaron Naughton kicked two first-half goals following his frightening tumble on his head in last week's loss against Sydney.
Fremantle will take the red eye home to Perth on Saturday morning before preparing for a Thursday night blockbuster against Hawthorn at Optus Stadium.
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