Prado also helped on defense by throwing out Paul Janish at the plate in the eighth inning to keep the Braves in front. Janish tried to score from second base on Brandon Phillips' single to left field.
"Oh, he won the game," Jurrjens said of Prado. "He hits a two-run homer and throws a guy out at home. He was the one who won the game today."
Prado's throw got to the plate first, but Janish appeared to slide home safely as catcher David Ross applied a high tag. Janish and manager Dusty Baker argued the call with home plate umpire Dan Iassogna.
"I had a great angle," Baker said. "I was down at the end of the dugout. Clearly, clearly it looked like he missed him. He missed him six inches to a foot. I could see it.
"It's a shame."
Janish said he didn't think Ross made the tag.
"I looked at the replay and upon review, I didn't realize the ball beat me by quite so much," Janish said. "So from the umpire's perspective, I can understand why it was such a close call. It was just a tough play and it happened so fast.
"I just didn't feel like he tagged me. But that's the way it goes."
Jurrjens (7-1), backing up the throw behind home plate, had a good view of the tag. He laughed when asked about Iassogna's call.
"It's a bang-bang play," Jurrjens said.
"I can't say a lot about that. I'm just happy it went our way."
Prado said he thought of Saturday night's 4-hour, 7-6 win over the Reds in 12 innings as he prepared to make the throw to the plate.
"The first thing that crossed my mind was I don't want to play extra innings again," Prado said.
The Reds lost two of three to the Braves to complete a 2-8 road trip. The Reds left Cincinnati a half-game out of first place in the NL Central and finished the trip five games behind first-place St. Louis.
Jay Bruce hit a drive to right-center in the second inning for the Reds' only run. It was Bruce's NL-best 15th homer.
Jurrjens lowered his NL-leading ERA to 1.51. The right-hander gave up six hits, struck out five and walked two in eight innings.
He has not allowed more than two runs in any of his first nine starts.
"J.J. gave us everything he had," manager Fredi Gonzalez said. "It was a good ballgame, good old-fashioned pitching."
Craig Kimbrel stranded two baserunners in the ninth for his 15th save. Kimbrel walked Joey Votto on four straight pitches to open the inning before giving up a two-out single to Fred Lewis, putting runners on first and second. Kimbrel struck out Ramon Hernandez to end the game.
Cueto blanked the Braves for five innings before walking Jordan Schafer to lead off the sixth and giving up Prado's seventh homer just over the reach of Lewis in left field.
Cueto (2-2) gave up five hits in eight innings.
"That's a shame that Johnny has to lose that game," Baker said.
Bruce had two hits one day after he was hitless in six at-bats while twice hitting infield grounders with the bases loaded in the Reds' 7-6 loss in 12 innings.
The Braves flubbed an opportunity after Alex Gonzalez and Ross had one-out singles in the fifth. Jurrjens dropped a bunt in front of home plate which catcher Hernandez grabbed before throwing to third baseman Scott Rolen to start a double play.
The Reds placed RHP Sam LeCure on the 15-day disabled list with a strained right forearm. LHP Tom Cochran was called up from Triple-A Louisville. Cochran is the fourth Reds pitcher to be called up in the last four days, following Daryl Thompson, Mike Leake and Jeremy Horst. ... The Braves recalled RHP Cory Gearrin from Triple-A Gwinnett and optioned OF Wilkin Ramirez to the same club. Gearrin was 1-1 with a 3.18 ERA in 10 games with Atlanta before he was optioned to Gwinnett on May 18.