The Team Penske driver, who led 76 of the 500 laps, held off Brad Keselowski by 0.391 seconds at the Bristol Motor Speedway.
It added to Logano's victories at the Duck Commander 500 and Toyota Owners 400 earlier this season.
Joe Gibbs Racing driver Matt Kenseth ended up third, while fourth-placed Jimmie Johnson (Hendrick Motorsports) was close to four seconds behind the winner.
Logano made the decisive pass on Kenseth with 44 laps remaining.
Hendrick Motorsports' Jeff Gordon remains top of the standings with 845 points, clear of team-mate Dale Earnhardt Jr (818).
Keselowski (776), Logano (761), Kenseth (751) and Johnson (726) make up the top six.