Morgan followed his brilliant century in Friday's second international at Brisbane with a half century from 54 balls but his was largely a lone effort in a tired and directionless England batting performance.
Tim Bresnan made an unbeaten 41 from 36 balls at the tail, hitting two sixes from the final over of the innings to add a little gloss to the England total.
Captain Alastair Cook made 35 in his best performance since the second innings of the fourth Ashes test, a series of six innings in which he has only twice reached double figures.
The England innings was effectively in decline from the moment Cook was caught by Glenn Maxwell from the bowling of Nathan Coulter-Nile in the ninth over after he and Ian Bell had shared a rare 50-run opening partnership.
Cook had seemed comfortable at the crease for the first time in weeks when he stepped onto the back foot and drove a short ball from Coulter-Nile directly to Maxwell at cover.
England took the gamble of promoting Ben Stokes to No. 3 in the hope the all rounder might provide some early momentum but that step failed when Stokes took 39 balls to make 15 with no boundaries before being superbly caught by Michael Clarke off Xavier Doherty.
