Morgan, a sophomore from Scotland, fired a 1-under-par 71 to help the ninth-ranked Eagles overcome a seven-shot deficit and win the initial meet of their spring campaign.
Morgan captured medalist honors at 5-over 149 for a one-shot victory in the 36-hole event. Sam Lockhart of Kirkwood tied for fourth place at 10-over 154.
Kirkwood finished five strokes ahead of William Woods, 621 to 626, for the title. The Eagles shot a team score of 323 on Monday in the first round but improved by 25 shots to post a 298 on Tuesday.
TEAM STANDINGS: 1. Kirkwood 621, 2. William Woods 626, 3. Evangel 645, 4. Ave Maria 664, 5. College of the Ozarks 676, 6. Westminster 687, 7. Hannibal-LaGrange 688.