Roger Bernadina doubled in Cincinnati's other run.
The Reds opened the second with singles by Jay Bruce, Todd Frazier and Bernadina, loading the bases for Mesoraco, who made it 4-1. Mesoraco's other grand slam came against Atlanta on May 24, 2012.
Arizona got two runs in the third. With two outs, Pollock lined one past Frazier at third base. It was originally ruled an error but later changed to a double. Gerardo Parra followed with an RBI single. He took second on the throw home, then scored when Frazier fielded Paul Goldschmidt's slow bouncer and threw it high over the head of Bernadina at first and into the Reds' dugout.
The Reds got a run in the sixth on Bernadina's RBI double, and Arizona answered with one in its half of the inning. Aaron Hill singled home Goldschmidt from second, leaving runners at first and third with one out.
Chris Owings struck out, then Inciarte was called out at first with Leake taking the throw from second baseman Brandon Phillips and covering on a close play. Manager Kirk Gibson challenged the call but it was upheld on review. The tying run would have scored had the challenge been successful.
"That was a huge play right there," Cincinnati manager Bryan Price said. "I wouldn't say a game-saver, but maybe a game-changer for sure."
NOTES: The Reds' Billy Hamilton stole his 19th base of the season. ... When Miguel Montero threw out Bernadina trying to steal third in the sixth, it was just the third caught stealing for the Arizona catcher in 28 tries. ... In the third game of the series Saturday night, the Reds have Johnny Cueto (4-4, 1.83 ERA) on the mound against Arizona's Brandon McCarthy (1-6, 4.87). ... Cincinnati is 26-11 with the roof closed at Chase Field, 5-12 with it open. It was open Friday night.