Evan Bush, Carlos Sosa, Rocky Scelfo, Gabe Scott and Zac Welch all homered to the lead the Crimson Tide to its first shutout since blanking Mississippi Valley State 21-0 last year.
The win also gives Alabama its 27th consecutive non-conference home series win under Jim Wells.
The five home also came in three different innings against three different UC pitchers.
Welch, a junior from Wellington, matched his career high four hits, including a pair of doubles and one home run. Welch's two doubles also tied a career high for the first baseman.
Scelfo, a junior second baseman from Lafayette, La., added two hits and four RBI, including a three-run home run to highlight the Crimson Tide's four-run fifth inning.
Bush, a sophomore left fielder from Rainbow City, added two hits and scored two runs for the Tide.
Alabama (4-2) scored the only runs it would need in the third inning to take a 2-0 lead.
Junior Mark Haske, playing his first game of the season in center field, doubled and scored when Sosa lined into an unusual double play, in which Allen Rice was forced out a second base on a fly out to left field.
Bush hit his second home run of the year to give Bama a 2-0 lead.
The two runs were more than enough for freshman left-hander Wade LeBlanc (1-1), who tossed seven shutout innings for his first collegiate win. The Lake Charles, La., was not as sharp on Saturday as he was in his debut last week, but still limited the Bearcats to five hits, while walking three and striking out four batters.
UC starter Greg Russell (0-1) was charged with the loss. The right-hander allowed two runs and six hits in three-plus innings. Kyle Markle allowed seven runs and eight hits in 3 2/3 innings out of the pen. Adam Curley was charged with two runs and three hits in his 1 1/3 innings on the mound.
Sosa, a senior from Vera Cruz, Mexico, led off the fifth with a solo home run, his second of the season. After Bush singled and Welch doubled, Scelfo hit his first home run of the year to make it a 6-0 game.
The Crimson Tide added four more runs in the bottom of the seventh to take a 10-0 lead. Welch singled and scored on Scelfo's RBI double into the left-field corner to make it 7-0.
Then, Alabama scored three runs with two outs to stretch its lead to double digits. Senior catcher Nick Richardson's sacrifice fly scored Scelfo and freshman shortstop Greg Paiml and Haske followed with two-out RBI singles.
Alabama closed out the scoring with the two more home runs in the eighth inning as junior left fielder Gabe Scott and Welch made it a 12-0 game with back-to-back homers off Curley.
Freshmen right-fielder Michael McCallister had a career-high three hits in the win for Alabama. The Green Cove Springs, Fla.., native singled in the second, doubled in the fourth and singled and scored in the seventh.
The Crimson Tide finished the game with 17 hits, the most since collecting 18 hits in a win over Arkansas last season.
Cincinnati (1-4) managed only six hits in the loss. The Bearcats stranded nine base runners in the game, including leaving the bases loaded against LeBlanc in the fourth inning.
Sophomore Matt Downs pitched the final two innings for Alabama, allowing one hit and striking out three batters.
The two teams close out this three-game series with a 2 p.m. game Sunday at the Joe. Alabama is expected to send freshman left-hander Brandon Belcher (2 G, 0-0, 11.57 ERA) to the mound, while UC is expected to starter right-hander Tom Maynard (1 GS, 0-0, 8.10 ERA.