Hinshaw, the Angels' 15th-round Draft pick in 2013,was 2-for-3 with three walks and an RBI. He also scored twice and stole two bases.
Hinshaw hit .270 in 124 games with Class A Advanced Inland Empire and Class A Burlington this season, but offense wasn't Hinshaw's only contribution to the victory.
In the bottom of the first, Hinshaw made a nice catch in deep center field while crashing up against the wall.
"I had a good jump on it and I just wanted to help out the pitcher," Hinshaw said. "I love helping those guys out as much as I can, because that's what we're out there for. Whenever I get the opportunity to save a run or two, I'm willing to do it."
Following Hinshaw's catch, which highlighted a 1-2-3 bottom of the first, Mesa blew the game open.
The Solar Sox drew a trio of walks and collected four hits in a decisive five-run second inning.
The first four batters of the inning reached base, but the big blow came when Addison Russell -- the seventh batter of the inning and MLB.com's fifth-ranked prospect -- drove in two with a single up the middle.
"It's really nice," Hinshaw said of the second. "It helps you, especially the pitchers. They don't have to worry about nitpicking, they can just fill the zone and let us play defense. Offensively, we're not going to take our foot off the pedal, but it definitely keeps us relaxed, we're not pressing to get that big hit."
In addition to Hinshaw, Mesa received contributions from a pair of Nationals prospects.
Pedro Severino, the Nationals No. 11 prospect according to MLBpipeline.com, went 4-for-5 with an RBI and a run scored.
In 94 games with Class A Advanced Potomac, Severino hit .247 this season.
On the mound, Nationals prospect Neil Holland -- who posted a 3.40 ERA in 46 appearances between Double-A Harrisburg and Triple-A Syracuse -- allowed two hits in 2 1/3 scoreless innings.
Scottsdale's lone offense came in the bottom of the second when L.J. Mazzilli, a Mets prospect, blasted a three-run homer out to left field.
The win is Mesa's sixth in their last seven games and puts the team, which has scored 20 runs in the past two games, a game over .500.
"It's different playing with a bunch of guys that you don't know," Hinshaw said. "Everyone probably wants to start off on a good foot and do a little too much, but now that we're gelling we're all comfortable and I think that's a big part in the team turning things around."