Along with Madison Bumgarner, who was promoted the same day as he was, Alderson is one of the top pitching prospects in the Giants organization. He led the California League with a 2.79 ERA in 2008, and was 1-1 with a 4.15 ERA this season.
After such a promotion, there's a certain amount of pressure to prove yourself, Alderson said.
"I definitely felt a little bit of that. Our pitching coach, Ross Grimsley, calmed me down a little. We had a talk and he told me not to try to do too much. I just tried to keep learning every inning."
With one out in the first, New Hampshire's Brad Emaus lofted a fly ball to right field, which was misplayed in the wind by Eddy Martinez-Esteve.
Alderson struck out the next two hitters to end the inning, then fanned the first two he faced in the second.
"My fastball command was a big part of [the performance]. I was able to save my other pitches for later in the game and keep the hitters off balance," he said.
The 20-year old coasted into the seventh, when he surrendered a one-out walk to David Cooper.
"I was a little tired toward the end," Alderson admitted, crediting Grimsley and manager Steve Decker for their encouragement. "They told me, 'If you're running out of gas, just keep the ball down. Don't overthrow.'"
After getting a line-drive out to left field off the bat of Brian Dopirak, Alderson was relieved by Joe Paterson, who retired Adam Calderone to end the inning.
"It was the right decision to bring in the left-hander to face the lefty," Alderson said. "And luckily, the bullpen was able to close out the game for the win."
Jesse Foppert replaced Paterson in the eighth and allowed a two-out single, the only hit of the game for the Fisher Cats.
Southpaw Matt Yourkin entered the game with runners on first and second and one out in the eighth. He induced a ground ball from Brian Jeroloman and struck out Cody Haerther to record the save.
The Mother's Day outing "was up there" with the best games Alderson has ever pitched, he said.
"I talked to [my mother] before and after the game," he said. "It was tough not being with her on Mother's Day, but it was great to know she was listening while I was out there pitching for her."
Alderson's performance may have ratcheted up the pressure for Bumgarner, who makes his Double-A debut Monday against the New Britain Rock Cats.
"He came up to me after the game and said, 'Great. How am I supposed to top that?' [He threw] a lot of games like that [for the Class A Augusta GreenJackets] last year, and that's how I always felt."
"It's good for me to sort of turn the tables on him now, but he'll probably go out and do the same thing [Monday]."