McCarthy, who suffered a skull fracture and a brain contusion, allowed one run on three hits in his two innings of work.
McCarthy struck out Billy Hamilton to start the game, and after allowing a single to Brandon Phillips, he fanned Joey Votto and Ryan Ludwick.
The D-backs gave McCarthy a lead to work with as they scored three runs in the bottom of the first off Johnny Cueto, who worked two innings in his first action since straining his right oblique in last year's National League Division Series. Cueto surrendered four runs (two earned) on five hits, walking one and striking out one.
Aaron Hill had the key hit in the inning with a double off the left-field wall that scored Adam Eaton and Martin Prado.
The Reds got on the board in the second when Eaton had trouble tracking down a Denis Phipps fly ball in center that was scored a triple. Neftali Soto drove Phipps home with a sacrifice fly.
The D-backs increased their lead to 4-1 in the second when Cliff Pennington tripled and scored on Prado's single to right.
The Reds, though, battered reliever Starling Peralta in the sixth.
Kristopher Negron tripled home a run, Votto had an RBI single, Donald Lutz drove home a pair with a double and Henry Rodriguez added an RBI single for the Reds as they took a 7-4 lead.
The Reds' Yorman Rodriguez went 2-2 with three RBIs and a home run.
Reds up next: The Reds will be split up on Thursday, hosting the D-backs in Goodyear, Ariz., and sending a squad to Scottsdale, Ariz., to meet the Rockies. The home game begins at at 3:05 p.m. ET, while the away contest starts at 3:10 p.m. ET. Mike League will get the start in Goodyear while Aroldis Chapman gets the nod in Scottsdale for his spring debut. Jay Bruce (right heel) and Todd Frazier (left calf) didn't play Wednesday, but neither injury is considered serious.
Steve Gilbert is a reporter for MLB.com. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.