In the opener, the Express used three home runs off Zephyrs starter Omar Poveda to overpower the Z's, 5-4.
Matt Kata laced a two-run single through the hole at short with two outs in the top of the first to put Round Rock on top, 2-0.
Poveda wriggled out of jam in the second inning, keeping Round Rock off the board after the Express loaded the bases with none out.
The Z's responded by taking the lead in the bottom of the frame. Luke Montz drew a two-out walk from Express starter Greg Reynolds, and after Shawn Bowman ripped a single up the middle, Chase Lambin belted his eighth home run of the season onto the berm in right field.
Joey Butler made sure the lead was short-lived, however, by drilling a 2-2 offering from Poveda the opposite way to knot the score.
Leonys Martin and Brad Nelson homered back-to-back with one out in the fourth, giving the Express a 5-3 lead.
New Orleans answered with a run in the bottom of the fourth, when Bowman doubled over the head of Martin in center to score Mike Cervenak, who had led off with a single.
But the Z's could get no closer, as nine of the last 10 Zephyrs batters were retired, including all three in the seventh via strikeout by Express closer Tanner Scheppers, who earned his 10th save.
Reynolds (11-8) picked up the win, allowing four runs and six hits in six innings.
Poveda (4-3) suffered the loss, yielding five runs and nine hits in four innings. He walked two without a strikeout.
Round Rock struck early in the nightcap, taking the lead after just two batters against Z's starter J.D. Martin, who gave up a leadoff single to Leonys Martin, and a home run to Yangervis Solarte.
New Orleans got a run in their half of the first, capitalizing on a leadoff walk to Gil Velazquez, who went to third on a double by Chris Coghlan and scored on a sacrifice fly by Cervenak.
The Express regained a two-run advantage in the fourth, when Kata led off with a single, and came around to score after left fielder Chris Aguila allowed a ground ball single by Ryan Spilborghs to slip beneath his glove and roll to the wall for a two-base error.
New Orleans squandered an opportunity to possibly tie the score or even take the lead in the fifth, loading the bases with nobody out before Neal Cotts struck out Velazquez and Jeff Dominguez, and got Coghlan to fly out to escape unscathed.
As in the first game, the Zephyrs did not threaten again, seeing the final seven batters set down, including a pair of strikeouts from Yoshinori Tateyama in the seventh inning for his sixth save.
Cotts (2-1) was credited with the win, and Martin (6-9) took the loss, despite pitching a seven-inning complete game.
Oklahoma City beat Albuquerque, and in the process passed the Zephyrs for second place in the division, 3 1/2 games behind the Isotopes. The Zephyrs' "tragic number," either Isotopes wins or Z's losses, to be eliminated from postseason contention has dropped to two.
The Zephyrs and Express resume the four-game set on Wednesday at 7:05 p.m., with left-handers Brad Hand and Chad Bell getting the starting assignments.