It proved to be the magic wand for the Suns (54-63, 18-28 second half), who took over the game from that at-bat. Hagerstown started the game with two prime scoring opportunities but only managed two runs.
Hague's hit popped the cork for the offense.
"That was a huge knock," said Suns manager Matt LeCroy. "He fouled off a couple of nasty pitches. He laid off a couple of nasty pitches to get to the one he wanted. And then the guy got one up and made a mistake."
With the game tied at 2, Stephen King reached on a one-out single and Eury Perez added a two-out single to put runners on first and second. Hague cashed in as the Suns scored three of their seven runs with two outs.
"I do think hitting is contagious, but at the time I was just trying to hit the ball and drive in a run," said Hague, the Washington Nationals' third-round pick in this year's draft. "But the hit got us a two-run lead and got us going."
The hit allowed Suns starter Evan Bronson to work with a lead he didn't waste. He allowed two runs on four hits in five innings, before giving way to Luis Garcia. Garcia allowed one hit over three innings before Rob Wort closed out the game by setting down Greensboro in order -- including two strikeouts -- in the ninth.
"We played a solid game," LeCroy said. "We pitched well. Bronson did a job and Garcia did well. We have been playing a lot better baseball than we had been in the last week."
The Suns took a 1-0 lead in the second when Stephen King hit into a bases-loaded double play. Hagerstown doubled the lead in the third on consecutive two-out singles by Adrian Sanchez, J.P. Ramirez and Destin Hood.
Greensboro (54-61, 22-23) tied the game in the fourth when Wes Long hit an infield single up the middle with the bases loaded and Kyle Jensen lofted a sacrifice fly off Bronson, who got himself in trouble with two walks.
After Hague's triple, the Suns added two runs in the fifth by loading the bases again before King drew and RBI walk to chase Olmos (3-6). Justino Cuevas greeted reliever Chris Peterson with an RBI single to right for a 6-2 lead.
The Suns capped their scoring in the eighth on a single by Sanchez, followed by Ramirez's RBI double to right.
Hagerstown collected 13 hits, with Sanchez, Ramirez, Hood, Cuevas and Perez notching two each. Olmos allowed six runs on eight hits over 4 1/3 innings for the loss.
But everything seemed to get easier for the Suns after Hague's triple.
"He's a battler," LeCroy said. "He's a college guy and you can expect that from him. When he got that big knock, it picked everyone up. Everyone started squaring up on the ball and people started hitting."