Van Rooyen kicked two majors in a four-minute span early in the final term and then added the sealer in his side's 15.6 (96) to 11.12 (78) win at the MCG on Monday night.
Richmond, inspired by Noah Cumberland's three-goal first quarter, led by 25 points before halftime in front of 83,985 fans.
But the Tigers (1-1-4) coughed up nine goals to three after the main break in a fourth straight defeat that leaves their season hanging by a thread.
Making matters worse for Damien Hardwick's side, Maurice Rioli Jr hobbled off in the final few minutes with a hamstring issue.
Gun midfielders Clayton Oliver (32 disposals, six clearances), Jack Viney (30, five) and Christian Petracca (26, three) all shone for the Demons and Michael Hibberd put the clamps on Cumberland after quarter-time.
Captain Max Gawn was influential on return from a knee injury, claiming six contested marks and kicking a late goal, and helped ruck partner Brodie Grundy turn the game.
"It was a win full of character, coming from 25 points down," Demons coach Simon Goodwin said as his side advanced to a 4-2 record.
"Sometimes you've got to win differently and tonight was one of those times.
"You can start to build on these experiences as the year goes on and I think that's really important for us as a club."
Small forward Kade Chandler kicked three goals - all after halftime - and put Melbourne in front early in the final quarter.
In his fourth senior game, van Rooyen took a towering grab with a ride on Noah Balta to set up his first goal and added a second soon afterwards.
The 20-year-old had just four touches in the first three quarters before bursting to life.
"It's a great thing for Jacob," Goodwin said.
"At three-quarter time he certainly wasn't having the best night and at one stage we were thinking about subbing him, so thank God we didn't do that.
"He managed to turn it around ... and he had a really good last quarter."
Richmond were well served by veteran forward Jack Riewoldt (four goals) and Tim Taranto (33 disposals, six clearances) was busy, as was speedster Jayden Short (30 touches) on return from a calf injury.
But the Tigers kicked 1.5 in the final quarter and were left ruing missed chances throughout the match.
Superstar Dustin Martin was off target, kicking 1.3 from his 25 disposals.
"We've got to get better in areas that we can control," Hardwick said.
"We always call it 'Richmond hurting Richmond' and I thought we had a couple of them tonight, but what I couldn't question was our side's intent.
"They played with great spirit and it was a good, hard, tough game but we just weren't good enough for long enough."
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