The Blue Jays' No. 3 prospect Anthony Alford, ranked No. 86 on MLBPipeline.com's Top 100 Prospects, along with Toronto's No. 30 prospect Danny Jansen, sparked the offense.
Greene escaped trouble often during his three innings, walking three and giving up three hits but yielding only one run as he struck out two Surprise batters.
"I tried to keep my fastball down in the zone, and usually that's an effective way of getting ground balls," Greene said. "My approach is to try better at getting ahead ,and making sure that my thought process is right.
"I don't want to change anything, but just throwing my secondaries and locating my fastball to where I want it to go."
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Greene is accustomed to getting out of jams. He began 2016 with Class A Advanced Dunedin, but was called up to Double-A New Hampshire midseason. With Dunedin, Greene went 4-4 with a 2.90 ERA even though he sported a 1.44 WHIP, as he walked 38 batters over 77.2 innings. In Double-A his control issues continued as he walked an additional 33 batters in 68 2/3 innings en route to a 6-5 record with a 4.19 ERA.
After Greene's three innings, the Solar Sox tallied their first run of the day in the top of the fourth inning on an RBI groundout by Alford, tying the score at 1.
Two innings later Jansen drove in Alford and Juan Kelly, another Toronto prospect, to take a 3-1 lead, and the Solar Sox never looked back.
The 2016 season was a rough one for Jansen, as a hamate bone injury in his wrist forced him to spend multiple stints on the disabled list. He played in only 54 games for Dunedin, hitting .218 with a .313 OBP. Despite the injury, the 6-foot-2, 225-pound catcher stole seven bases.
Jansen is happy that he can finally swing the bat with ease after dealing with the injury last year.
"It feels good to be 100 percent for once, and I'm hoping to stay that way going into 2017," Jansen said. "They took the hamate bone out, and I let the stitches and soft tissue heal. There's no more bone to break anymore so it's good to go.
"I come every day ready to work, and I'm going to continue to work on getting my foot down on time and find the barrel. Today, I got enough of the bat on that first hit to drop down there and score two runs."
Toronto prospects accounted for four of Mesa's eight hits, while knocking in all three of their runs. Alford and Kelly each added a stolen base as well.
Alford enjoyed a sensational 2015 season with Dunedin, where he hit .302 over 57 games and 20 of his 68 hits went for extra-bases, including six triples.
2016 wasn't as kind to the highly touted prospect. Alford remained with Dunedin, hitting .236 over 92 games with two triples.
For Class A Lansing last season, Kelly had a .274 batting average, smacked 12 home runs and drove in 67 runs. He was also a perfect 11-for-11 on stolen-base attempts.