Lough had entered the game the previous inning as a pinch hitter, but was still at-bat because Elliot Johnson was picked off first base to end the ninth.
Lough singled off Braves reliever Alex Wood (0-2) to start the 10th and then reached second when Miguel Tejada laid down a perfect sacrifice bunt.
That set the stage for Gordon, who homered earlier in the game.
He dropped a base hit into shallow left field, allowing Lough to score easily as the Royals spilled from their dugout.
Aaron Crow (4-3) worked the 10th inning for the Royals, who had lost five of their past six. It was the sixth time in the past eight games that Kansas City played a one-run contest.
The Royals were actually in control through six innings.
Gordon ended a 159 at-bat homerless drought with his first-inning shot, the first leadoff homer of the season for the Royals. It was Gordon’s first home run since May 9 at Baltimore.
Billy Butler added a two-out double to right, and then the big DH chugged home when Salvador Perez got just enough of the bat on a pitch from Mike Minor to hit a single to left field.
The Royals tacked on another run in the third when Gordon singled to lead off the inning. Alcides Escobar put runners on the corners with nobody out before Eric Hosmer lined into a double play, but Butler managed to bring Gordon home with a timely single to make it 3-0.
That was all the offense until Luis Mendoza started to unravel in the seventh inning.
The Royals starter kept the Braves off balance with a mixture of fastballs and sliders, and had given up just three hits to that point. But he’d put runners on the corners with two outs when he was lifted for left-hander Bruce Chen, who promptly served up an RBI single to pinch-hitter Reed Johnson.
Chen walked Jason Heyward to load the bases and was replaced by right-hander Luke Hochevar, who gave up a tying two-run single to Justin Upton. Heyward was thrown out at third on the play to end the inning.
Minor allowed three runs on nine hits over six innings, while Mendoza gave up two runs on five hits over 6 2-3 innings. Neither of them factored into the decision.
Instead, it came down to a duel between bullpens.
Alex Avilan and Jordan Walden breezed through the Royals lineup, the only blip coming when Mike Moustakas singled off Walden with two outs in the ninth inning. Johnson came in to pinch run and strayed too far from first base, allowing Walden to pick him off and end the inning.
Hochevar wound up going 1⅓ innings for the Royals, who brought in star closer Greg Holland to pitch the ninth inning. He struck out the side on 11 pitches.