Recruit Jay Kennedy-Harris starred with two last-quarter goals as the Demons stunned the Tigers 1.13.11 (98) to 1.10.15 (84) on Friday night at Etihad Stadium.
Adding to a poor night for Richmond, veteran utility Chris Newman hurt his knee in the third term.
Newman had kicked two goals before he hyper-extended his left knee in a marking contest during the third term.
He was able to gingerly walk off the field without help, but went straight to the rooms.
The Tigers were pressing late in the match when David Astbury shanked a centering kick.
Kennedy-Harris pounced and took a couple of bounces before he goalled to ice the match.
Jeremy Howe then finished off with his fourth goal.
While it was only their first pre-season game, Melbourne showed great signs under Roos' coaching.
They had an astounding 445 possessions to Richmond's 262.
Their ball movement looked much more fluent and there was no drop-off in workrate.
While Newman kicked the opening goal of the game after a minute, Melbourne started better.
But the Demons were wayward, kicking 1.7.
Ben Griffith kicked a supergoal for Richmond as they led by 10 points at the first change.
Melbourne had to wait until late in the quarter for Howe to kick their first goal and clearly were missing key forwards Chris Dawes, Mitch Clark and Jesse Hogan.
Tyrone Vickery kicked two goals early in the second term, the first thanks to Jake Spencer's embarrassing turnover and the second after a mark.
But the Demons kicked the next three goals, including a nine-pointer to Cam Pedersen, and took the lead for the first time at 14 minutes.
Howe kicked his third goal close to halftime and Melbourne trailled by only five points at the long break.
The two teams went goal-for-goal in the third term, with several sprayed shots.
Rohan Bail snapped accurately just before the three-quarter time siren to give the Demons a five-point lead.
Melbourne key position player Jack Watts was a late withdrawal, apparently because of illness.
MELBOURNE 0.1.7 1.5.8 1.8.9 1.13.11 (98)
RICHMOND 1.2.2 1.6.7 1.7.10 1.10.15 (84)
Nine pointers: Melbourne - Pedersen. Richmond - Griffiths.
Goals: Melbourne - Howe 4; Kennedy-Harris 3; Bail 2; Spencer, Trengove, King, Blease. Richmond - Vickery 3; Miles, Deledio, Newman 2..
Best: Melbourne - Jones, Trengove, Kennedy-Harris, Vince. Richmond - Martin, Houli, Vickery, Miles.
Umpires: Stuart Wenn, Jacob Mollison, Scott McPhee.
Official Crowd: 12,024 at Etihad Stadium.