The Demons got off to flyer when co-captain Nathan Jones snapped a goal under pressure and out of the pack.
But the rest of the term was a low-scoring affair, with just two more majors added – both to the Tigers via Daniel Jackson and Shane Edwards.
At the first break, Richmond led by six points.
The Tigers led by 11 points early on after Jack Riewoldt opened the term.
But when Jack Watts kicked Melbourne’s second at the 10-minute mark, it was the start of three in row for the Demons. Matt Jones and Aidan Riley – making his debut for the red and blue – followed up, as Melbourne hit the front for the first time, claiming a six-point lead.
But when Shane Edwards kicked his second in time-on, the Tigers reclaimed the lead by three points at half-time.
The Demons started the second half strongly, booting the first two goals – courtesy of Dom Tyson and Chris Dawes – to gain an eight-point advantage.
But when the Tigers kicked consecutive goals, they were back in front by six points.
However, the Dees answered again, this time through Cam Pedersen and Jack Viney, who put them up by eight points at three quarter-time.