The Demons went down 12.10 (82) to 12.14 (86).
In a match marred by poor skills and disposal errors, the final term delivered pulsating action.
Richmond kicked the first two goals to wipe out Melbourne's eight-point lead, but when Nathan Jones and Brad Miller kicked truly, the Demons were back in front by two points.
Entering time-on it became anyone's game, but when Nathan Brown bobbed up with his third and Brett Deledio jagged his second, the Tigers were up by 10 points at the 23-minute mark.
Enter Jack Grimes and Ricky Petterd, who kicked goals at the 26 and 27 minute marks respectively, to again put the Demons in front.
With only a minute remaining, Richmond made one final charge. With the ball in the Tigers' attacking zone, Richard Tambling hit teammate McMahon in the centre corridor as the siren sounded.
McMahon went back and nailed Richmond's third win under caretaker senior coach Jade Rawlings.
For the Demons, dual Keith Truscott Trophy winner and first-year Melbourne skipper James McDonald played his best match for the season. He notched up 16 touches by half-time and finished with 28 disposals – a game-high.
Cameron Bruce and Petterd both had 25 touches each, while Matthew Bate (23) was also among Melbourne's best. Grimes also continues to blossom as one of Melbourne's most promising players and Lynden Dunn impressed with two goals.
Cousins was Richmond's highest ball-winner with 27 touches, while Deledio (24) and McMahon (23) were also prominent. Brown jagged three for the Tigers.
Already troubled by injuries to key personnel, the Demons lost young gun Cale Morton before the start of the match through illness. Richmond went in unchanged.
Versatile big man Stef Martin suffered a calf injury in the first term and although he played on, he was troubled by it for the rest of the day. Youngster Jamie Bennell also finished the day on the bench in his tracksuit.
The Tigers also had their injury concerns with Jack Riewoldt (second term) and Luke McGuane (third quarter) suffering shoulder problems, but both played out the match.
Tenacious Tiger Jake King took on Demon dangerman Aaron Davey from the word go. The duo started on the wing and tangled in the first term, with King booked for wrestling Davey.
The opening term was hardly one for the archives.
It took nine minutes before the first major was registered via Mitch Morton, who kicked Richmond's only goal for the quarter.
Melbourne opened its account mid-way through the term courtesy of Neville Jetta. And when Lynden Dunn followed up soon after, the Dees led by one point at the first break.
The tempo lifted a little in the second term, as Richmond gained an 11-point lead in time-on – the biggest lead in the first half. But when Michael Newton kicked a soccer goal at the 27-minute mark, the Demons were back within five points at half time.
The third quarter saw some entertaining footy and provided highlights when Davey and Dunn both kicked remarkable goals.
Davey slotted through a beauty on the run from the boundary line at the Great Southern Stand End, while Dunn soon followed up with a brilliant dribble kick, tucked in the pocket.
Seven goals were scored for the term, with Melbourne kicking 4.4 to 3.2 to take a three-point lead into the thrilling final term.
Unfortunately for the Dees, the advantage was just not enough.
Melbourne 2.0 4.3 8.7 12.10 (82)
Richmond 1.5 4.8 7.10 12.14 (86)
GOALS
Melbourne: Dunn 2, Miller 2, Petterd 2, Jetta, Bate, Newton, Davey, Jones, Grimes
Richmond: Brown 3, Morton 2, Deledio 2, Vickery, Nahas, Riewoldt, Hislop, McMahon
BEST
Melbourne: McDonald, Bate, Petterd, Whelan, Bruce, Grimes
Richmond: Deledio, Jackson, Brown, Cousins, Edwards, King, McMahon
INJURIES
Melbourne: Morton (illness) replaced in selected side by Spencer, Bennell (knee), Martin (corked calf), Whelan (foot)
Richmond: Nil
REPORTS
King (Richmond) reported by umpire James for wrestling Davey (Melbourne) in the first quarter
Davey (Melbourne) reported by umpire James for wrestling King (Richmond) in the first quarter
Umpires: Farmer, James, Keating
Official crowd: 37,438 at the MCG
The views in this story are those of the author and not necessarily those of the clubs or the AFL.
