Reds right-hander Homer Bailey gave up three runs over a four-inning start and left with a 7-3 lead, but the Mariners rallied off Clay Hensley for four runs in the fifth, helped by Morse's three-run shot just over the left-field fence.
Mike Zunino, one of the Mariners' top prospects, erased a 7-7 tie in the eighth with a solo homer, his second of the spring.
The Mariners increased their Cactus League-leading home run total to 36 in 19 games.
Morse left no doubt on his first blast, a two-run bomb just to the left of the batter's eye in center field off Bailey, whom he faced previously while with the Nationals the past four years.
"He's a really good pitcher," Morse said. "He locates his fastball really good. I think he was trying to locate that one down a little more to try to get me into a double-play ball, but he left it up a little and I got a good piece of it."
Bailey, making his fourth start of the spring, allowed six hits with no walks and one strikeout while throwing 57 pitches.
Mariners lefty Joe Saunders gave up seven runs (five earned) on nine hits in his second Cactus League start. The newly signed free agent was lifted after 3 2/3 innings when the Reds pushed across three runs in the fourth with a walk and four hits, including a pair of doubles.
The Reds totaled four doubles off Saunders, including two by left fielder Denis Phipps, who went 2-for-3 with two runs scored.
Brandon Maurer, having a strong spring this year as a 22-year-old right-hander, shut out the Reds for four innings in his longest appearance yet. Maurer allowed three hits with two walks and four strikeouts, putting his spring ERA at 0.90 with one run allowed in 10 innings.
Shortstop Zack Cozart went 2-for-4 with a double and two RBIs for the Reds. Joey Votto, playing his second game since returning from the World Baseball Classic, went 0-for-2 before being replaced in the fourth inning.
First baseman Justin Smoak and designated hitter Kendrys Morales each went 2-for-3 with an RBI for the Mariners. Smoak is hitting .375 this spring and Morales .355.
Cozart, Phipps, Chris Heisey and Jason Donald had two hits apiece for the Reds.
Up next: The Mariners' two comeback pitchers -- Jon Garland and Jeremy Bonderman -- are both scheduled for four-inning outings on Friday as Seattle plays a pair of games. Bonderman, attempting to make the squad after not pitching in the Majors since 2010, will start the Cactus League game at 1:10 p.m. PT in Tempe against the Angels. Garland, who had shoulder surgery in 2011, faces The Netherlands in a 7:05 p.m. exhibition game at Peoria Stadium. Garland has been outstanding this spring, allowing one run and five hits in six innings. Bonderman has given up six runs and eight hits in six innings, but has been getting stronger in recent outings after having Tommy John surgery 10 months ago.