Jose Ramirez had two hits in his return from a two-game suspension for punching Tim Anderson of the Chicago White Sox.
Allen (6-5) was effective for a third straight start, holding the Reds to four singles while striking out seven. The lefty has allowed just three runs and 12 hits over 17 innings in his three August starts.
Enyel De Los Santos, Trevor Stephan and Emmanuel Clase combined to hold the Reds to two baserunners over the final three innings. For Clase, it was his 32nd save in 41 chances as Cleveland won back-to-back games for the first time since a three-game win streak July 25-27.
For the Guardians, it was their 15th win in their past 19 games in Cincinnati.
Losing for the 10th time in 13 games, the Reds could only manage six hits in the opener of the brief two-game series.
The Guardians jumped out to a 2-0 lead in the opening inning as four of the first five batters reached against Cincinnati starter and loser Graham Ashcraft (6-8).
After Steven Kwan singled to center to open the game, Ramirez lined a pitch to Spencer Steer in left. Steer lost the ball in the setting sun and it got past him for a double that put runners on second and third.
Following a strikeout by Andres Gimenez, Kole Calhoun singled to left to score Kwan and Ramirez for a two-run Cleveland lead.
The Reds had a golden opportunity to get back into the game in the sixth. Matt McLain walked, and Elly De La Cruz reached on a single when second baseman Gimenez unsuccessfully tried a no-look, back-flip toss to shortstop Gabriel Arias covering second.
But on a Steer flyout to right, De La Cruz was thrown out trying to tag and advance to second as McLain advanced to third. The inning ended on Henry Ramos’ strikeout.
The Guardians answered immediately in the seventh against Ashcraft when Kwan drove in Myles Straw for a 3-0 lead.
—Field Level Media