The win gave Washington a 6-3 mark on its nine-game road trip and marked the Nats' fifth series win in their last six. The loss concluded a miserable 2-8 homestand for Atlanta.
Ortiz (5-4), who entered the game 0-3 with an 8.53 career ERA against Atlanta, allowed two runs and six hits, while striking out five in 6 2/3 innings.
"It's something nobody could predict," said Nationals manager Frank Robinson of the resurgence of Ortiz, who was hammered for six earned runs in 6 1/3 innings in his May 12 loss to Atlanta at Turner Field. "It's enjoyable to watch. It's just been kind of unbelievable. It's like a different person."
Smoltz, who came into Wednesday night with a 16-7 lifetime record against the Nats/Expos, dropped to 4-4 in 2006, suffering his second straight loss. He has just one win in his last five starts.
The Nationals broke a scoreless tie with three runs in the sixth, on two-out doubles by Nick Johnson and Ryan Zimmerman, followed by Anderson's second homer of the year.
"It was a slider," said Anderson, who is now hitting .328 (9-for-28) lifetime against Smoltz, of his homer. "I was able to battle there and lay off the sinker away the pitch before, and got a slider that he left up a little bit."
"We've hit him all right the last couple of times," added Zimmerman, who went 1-for-2 and is now hitting .400 (4-for-10) against Smoltz in his career. "He's always going to be there late in the game. He's that kind of pitcher. But [tonight was big] for our confidence and just what we can do. It doesn't matter who's on the mound, we can win every night. It was good to get a win against someone like that."
The Braves got a run back in their half of the sixth, on Adam LaRoche's two-out RBI single, then closed to within 3-2 in the seventh when pinch-hitter Pete Orr belted a 1-0 pitch into the stands in right-center.
Second baseman Marcus Giles followed the homer with a triple to right-center as his fly ball fell at the wall between converging outfielders Damian Jackson and Marlon Byrd. Jackson was shaken up after hitting the wall, but stayed in the game.
The delay, while trainer Tim Abraham and Robinson went out to check on Jackson actually turned out to work to the Nats' advantage.
"I don't know if [Gary Majewski] would have been ready or not," admitted Robinson. "On the way back, I said, 'This is kind of a little blessing.' It gave him a chance to really make sure he was ready. I didn't even check. That's how sure I was that he was ready."
Majewski relieved Ortiz, who has now pitched into the seventh in four straight starts, and struck out Edgar Renteria to end the threat.
Washington put the game away in the eighth, loading the bases against reliever Macay McBride on an infield hit, a walk and an intentional walk, then Ward delivered a two-run double inside the left-field line off reliever Tyler Yates in what Robinson called "a great at-bat, exactly what we needed."
"I told myself, 'I just need a base hit to come through for the team here,'" said Ward, who broke an 0-for-5 slump as a pinch-hitter. "I was able to poke a sinker into left field. It was the first ball I hit to left field all season. So it felt good."
Majewski, who has not allowed a run in his last four appearances, and Chad Cordero combined to retire the final seven Braves in a row, with Cordero pitching a perfect ninth to earn his second save of the series and his 11th in 13 opportunities.
Both teams threatened in the first and second innings but stranded runners in scoring position in both frames.
While the scoreless duel proved tense, temperatures rose in the bottom of the second when Ortiz hit Jeff Francoeur with a pitch on the left hand. As Francoeur walked to first with Atlanta trainer Jeff Porter, he and Ortiz exchanged glances then words, bringing several Braves to the top step of the dugout. Two ensuing pickoff attempts drew major boos, but then Ortiz retired the next hitter on a force play, with Francoeur earning applause for his hard takeout slide of Washington shortstop Royce Clayton.
In the end, it was the Nationals that did the upending, allowing for talk of Washington passing Atlanta for third place in the National League East.
"We're not going to say we have a good chance to overtake them," Robinson said, "but that's our goal -- to overtake the team in front of us first -- then you look to the next team."