Assistant-player-manager Dave Michaels gave Glenthorne the upper hand with two well-taken penalties in the first half.
Morris capped a virtuoso performance with a goal, with Gary Adams completing the scoring as EDRS suffered cup final heartbreak for the third consecutive season.
Michaels said: "As a team we defended excellently. Our five-man midfield and strikeforce worked very hard and I don’t remember EDRS having a chance in open play."
EDRS had beaten Glenthorne 3-2 in the league last week, but Michaels believes Glenthorne were worthy winners.
"The big, grass pitch suited us more than it did them and they simply couldn’t handle Greg Morris who terrorised them with his pace," said Michaels.
EDRS' Gary Shaw said: “Glenthorne were better but the two controversial penalties decisions knocked us for six."