Mesoraco's blast came in the sixth inning and put the Reds in front 5-2. Cincinnati completed a four-game sweep of the Braves and won for the sixth straight time overall.
This was the 39th major league game for Mesoraco, who became backup catcher for the Reds last year. His career batting average coming into the contest was .194.
Atlanta starter Randall Delgado (2-5) issued a walk to Brandon Phillips in the sixth, gave up a one-out single to Chris Heisey and walked Todd Frazier before Mesoraco hit a 2-0 pitch over the wall in left.
Drew Stubbs added a solo homer for the Reds in the seventh.
Homer Bailey (3-3) picked up the win with a six-inning performance. He allowed two runs on four hits and struck out six.
Logan Ondrusek put two runners on with one away in the ninth, but escaped the jam thanks to a double play and earned his second save.
Texas principal bans speaking Spanish, stirs controversy
Exploding whale video goes viral on Internet