Frawley went off with an adductor strain in the second quarter and Rivers with a lower leg injury after showing incredible courage backing into a contest in defence in the same term.
The Demons kicked just one goal in the opening quarter but fought back to trail by four points at half time and then led by as much as 11 points midway through the third.
Solid efforts three weeks in a row against West Coast, Geelong and Adelaide after a good win over Richmond would be little comfort for the Demons with the 13.4 (82) to 12.18 (90) loss to the Eagles leaving them on the bottom of the ladder.
Cale Morton and Cameron Bruce led the way through the middle and across half back with 34 and 33 possessions respectively, with Nathan Jones doing well for 27. Clint Bartram had 15 and did well on Daniel Kerr before the Eagle went off injured.
Jamie Bennell last played on Subiaco Oval in last year's WAFL colts grand final where he helped Swan Districts to a win and was exciting across half back with his 19 possessions.
Paul Johnson did a terrific job in his 50th game against his former side opposed to Dean Cox in the ruck. He had the big job with John Meese999n missing with a foot injury and finished with 20 possessions and 21 hit outs, opposed to Cox's 23 and 27.
Brad Miller kicked three goals all within five minutes in the second quarter, while Russell Robertson, Addam Maric and Ricky Petterd kicked two each.
The Demons looked certain for their first goal 10 minutes in when a Matthew Bate snap was on target with his non-preferred right foot, however, as it bounced right in the middle of a vacant goal square it went onto the goal line before veering towards the points.
Three minutes later the Dees did get in the board through Maric.
The Eagles got last goal of the term to lead by nine points, but within 50 seconds of the second a 50m penalty helped Bruce kick Melbourne's second.
The margin was again just three points when Bartram hurt Kerr the other way with a good running goal. Adam Hunter and Mark LeCras kicked quick goals to put the Eagles up by 15 points before Miller caught fire with three quick goals in four minutes.
His third put the Dees in front by two points for the first time in the match but was soured a little when Rivers was carried off the ground on a stretcher after an incredibly courageous act running back with the flight of the ball in defence.
Cox and Adam Selwood quickly responded with late goals to put West Coast back up by two goals, but a good snap from Bate just before the half time siren cut the margin to four points.
The Demons came out firing to start the third with Robertson kicking two goals and Jones another to see them 11 points up.
However, West Coast finished the term with four consecutive goals to lead by 15 at three quarter-time.
A tremendous running goal by Maric gave the Demons some hope again and brought the margin back to two goals but the Eagles steadied.
Melbourne kept coming and two pressure goals to Petterd gave the visitors hope, but they fell eight points short.
Melbourne still sits in last spot on the ladder with a 1-6 record after seven rounds and takes on a Western Bulldogs team next Saturday at the MCG who had a good win in Adelaide over the Crows also on Sunday.
The views in this story are those of the author and not necessarily the clubs.
West Coast 2.4 7.7 11.12 12.18 (90)
Melbourne 1.1 7.3 10.3 13.4 (82)
GOALS
West Coast: LeCras 4, Hunter 2, Cockie, Cox, McKinley, McNamara, Masten, Selwood
Melbourne: Miller 3, Maric, Petterd, Robertson 2, Bartram, Bruce, Bate, Jones
BEST
West Coast: Selwood, LeCras, Glass, Cox, Wirrpanda, Masten, Hurn
Melbourne: Jones, Bruce, Moloney, Miller, Morton, Bennell
INJURIES
West Coast: Eric Mackenzie (calf soreness) replaced in selected side by Will Schofield, Matt Priddis (thigh) replaced in selected side by Scott Selwood, Daniel Kerr (groin), Adam Cockie (ankle)
Melbourne: James Frawley (adductor), Jared Rivers (ankle)
Reports: Nil
Umpires: Margetts, Dalgleish, Schmitt
