Edwards, who missed qualifying at Memphis Motorsports Park because of practice for Sunday's Sprint Cup Race in Atlanta, started 34th in his No. 60 Roush-Fenway Racing Ford, but gained ground quickly after making an early stop for fresh tires.
He took the lead from Mike Bliss on Lap 69, and never trailed after that, taking his fifth Nationwide Series victory of the season and 18th of his career.
Edwards pulled within 116 points of series leader Clint Bowyer, who finished 16th. There are three races remaining on the schedule.
"Any time you can gain 80 points on that team you're doing something," Edwards said. "But obviously we've got to think about winning the next three races."
Kenny Wallace finished third, his best series finish since 2005 and the best finish ever for team owner Jay Robinson. He was followed by Austin Dillon, grandson of NASCAR team owner Richard Childress. It was Dillon's second Nationwide start.
Reutimann, who battled back from two laps down, kept his Toyota on Edwards' bumper for the final two laps couldn't overtake him for the lead in a green-white-checker finish brought on by Brian Keselowski's accident with four laps to go.
"It came down to the last couple of laps where I could have easily had gotten into his back bumper, moved him and gone on," Reutimann said, "but that's not the way I like to do things. It's not the way I was taught to race. Hopefully it will come back someday, but now it just feels lousy to lose."
Earlier, in the heat of the moment, Reutimann had said: "Long story short, I should've moved him. He would've moved me for sure."
Edwards has been involved in a number of incidents, including a Sprint Cup dustup with Kevin Harvick that led to a garage confrontation last month.
"My crew was telling me his guys were getting on him to bump me," Edwards said. "I'd go down low, and was waiting for the contact. To be honest, I'm not sure how I would have reacted before today if I were in his position. But from now on, he's got the free pass from me. David really earned my respect."
It was Edwards' first win on this three-quarter-mile oval.
"It's special, because this is where I ran my first NASCAR event in the Truck Series," he said. "That day I felt like the race went on forever, and I was exhausted when it was over."
Edwards and the lead pack held out to the last second on a round of green flag pit stops that started on Lap 92, and put the field a lap down at the halfway point of the race when Bowyer spun on the track, bringing out one of eight cautions. It was a much cleaner race than a year ago, when the yellow flag came out 25 times, one short of the series record.
Earlier in the day, 18-year-old James Buescher, in only his sixth career Nationwide Series start, grabbed the pole with a lap of 117.591 mph in his Toyota. He is the third-youngest polesitter in series history (18 years, 214 days), behind only Casey Atwood and Logano. He finished 19th in the race.