Daniel Nava added two hits and scored a run and Brock Holt scored a pair of runs for the Red Sox, who swept the two-game set and won all four games against the Reds this season.
Yoenis Cespedes added an RBI, but left the game with a sore right hand, as the Red Sox have won three straight and five of seven.
"He was fighting me a bit, but it was precautionary," said Boston manager John Farrell.
Called up from Triple-A Pawtucket to start for the struggling Brandon Workman, Anthony Ranaudo (2-0) picked up the win in his second career start. The right- hander surrendered four runs on eight hits over six innings.
"He gave us six solid innings," said Farrell "He's a fly ball pitcher and that's risky in this ball park. He battled."
Skip Schumaker homered, finishing 3-for-4 for the Reds, losers in four of their last five.
Cincinnati starting pitcher Mike Leake (9-11) also homered, but it wasn't enough to help him avoid his second straight loss. The right-hander was charged with five runs on eight hits over five innings, striking out three and walking one. The five runs allowed were his most since yielding five on June 10 against the Dodgers.
Trailing 3-2, the Red Sox put up a three-run fifth to take the lead. Cespedes' two-out single plated Holt, who started the rally with a one-out double, to tie the game. Napoli followed with a homer to put the Sox ahead 5-3.
The Reds got a run back in the home half of the frame when Todd Frazier's sacrifice fly plated Kris Negron, who started the inning with a triple, but that was it for the Reds.
Ranaudo finished up with the sixth inning and Burke Badenhop, Junichi Tazawa and Edward Mujica worked an inning each to wrap it up.
Mujica got out of a two-on, no-out jam in the ninth by striking out Ramon Santiago on a bunt attempt, getting Billy Hamilton to fly out and inducing a ground out by Negron to pick up his third save of the season.
The Red Sox got going with a pair of first-inning runs courtesy of a Nava RBI single and Napoli fielder's choice grounder.
The Reds cut the deficit to 2-1 in the third when Devin Mesoraco's sac fly plated Negron and then took the lead, 3-2, in the fourth when Schumaker and Leake hit solo homers.