Ed Richards and Marcus Bontempelli starred in the midfield as the Bulldogs burst clear before halftime and resisted a fightback in their 14.9 (93) to 13.12 (90) victory at Marvel Stadium.
The Bulldogs threw away a 33-point second-quarter lead and trailed twice in the final term before Freijah kicked the go-ahead goal in time-on.
Demons young gun Harvey Langford had the chance to win the game but dropped a mark under huge pressure from Lachie Jacques close to goal.
The Dees had another chance with a kick back into full-forward but Lachie Bramble took what proved a match-saving mark for the Dogs, who steadied in the dying seconds.
Sunday's result lifted the Bulldogs (6-5) to ninth spot, just one win behind the Demons (7-4), who sit sixth.
But it came at a cost as defender Luke Cleary went off after a head knock in the second term and was ruled out with concussion.
Richards (30 disposals, three goals) and Bontempelli (29 disposals, two goals) were outstanding in the midfield along with Ryley Sanders (31 touches).
Bailey Dale (31 possessions) was also influential, while Rhylee West, Aaron Naughton and Arthur Jones (two each) also kicked multiple goals.
West's crucial run-down tackle on Jack Steele in the final quarter lifted his team and led to Freijah's goal.
Bulldogs coach Luke Beveridge lauded his team's response to being "touched up" in the critical areas of contest, clearance and territory in a shock loss to Carlton the previous week.
"You can imagine our mandate today and our focus was to fix all that up and represent in a better way as a team, and to a man I just thought the boys were outstanding," Beveridge said.
"It was probably just that few minutes at the end of the second quarter when Melbourne probably got a run-on with some of their brilliance that undid some of that good work.
"To win another close one gives us a lot of inner belief."
Melbourne star Kysaiah Pickett had 25 disposals and six clearances in an entertaining duel with Richards, while Tom Sparrow (23 touches) and Steele (21) fought hard.
Harry Sharp and Langford kicked two goals each, but Demons coach Steven King conceded the Bulldogs "brought the heat" and his side couldn't keep up.
"They played with a greater energy and intensity for longer," King said.
"We had it in patches but they started the game really strongly, especially around stoppage, which gave them great territory.
"You look at the ground-ball number and we were convincingly beaten. I think that's pretty indicative of us being close enough but not really impacting."
Melbourne lost experienced defender Jake Lever for the last 10 minutes after a head knock in a marking contest.
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