The Mariners' No. 3 prospect allowed two hits and one walk over six scoreless innings as the Generals blanked the Mississippi Braves, 7-0.
Walker struck out seven while walking just one. The game marked Jackson's first shutout of the season, as the Generals improved to 9-4 and lowered their team ERA to 2.29.
"I was just trying to locate my fastball and get ahead with it, and I was able to throw some breaking balls in there," said Walker, who is ranked as MLB.com's No. 18 prospect overall. "I think the biggest thing was me getting ahead."
After tossing a perfect first inning, Walker allowed two of his three baserunners in the second. Joe Leonard drew a one-out walk and Adam Milligan lined a two-out single to left field. Walker was able to escape the jam by inducing a flyout from Brahiam Maldonado.
"I just tried to slow down and go up there and make him put the ball in play," Walker said. "Get a groundball out or a pop fly out or something."
Starting with Maldonado, Walker retired 13 of the final 14 batters he faced. The only exception was Christian Bethancourt, who led off the fifth with a single to center field.
After going 6-5 with a 2.89 ERA and 113 strikeouts in 96 2/3 innings for Class A Clinton last year, Walker owns a 1.64 ERA through two starts this year. The 19-year-old right-hander has fanned 15 batters in 11 innings.
Reliever Jandy Sena took over in the seventh, allowing one hit over the final three frames to notch his first save of the year and the third of his three-year career.
Sean Gilmartin (0-2), selected by the Braves with the 28th overall pick in the 2011 Draft, allowed five runs on nine hits over six innings. Jackson's Jesus Sucre did most of the damage against him, delivering a three-RBI double in the second.
Walker, who was selected 43rd overall in 2010 and was named the Mariners' Minor League Pitcher of the Year last season, said he wasn't aware of Gilmartin's pedigree.
"I just try to worry about myself and about the team," he said. "I just try to go out there and give the team a chance to win. I don't really pay attention to who's pitching for the other team."
Joseph Dunigan also had a strong day at the plate for the Generals, going 2-for-4 with a two-run homer in the seventh that essentially put the game out of reach.
Though Jackson is known for its starting five -- with No. 2 Seattle prospect Danny Hultzen and No. 5 prospect James Paxton also in the rotation -- Walker pointed out that the rest of the squad is strong as well.
"Our hitters are really great, they've put up a lot of runs," he said. "That's always a plus, especially when we score early -- that gives the pitchers more confidence. Our pitching staff, I think we have a really good starting five, but even our bullpen is really good. That helps a lot. You can trust them."
Looking down the line, Walker thinks the big leagues are within his reach this year. But first, he's focused on staying healthy, as he made just 18 starts last season.
"The ultimate goal is to pitch in the big leagues this year," Walker said. "But I just want to go out there and record innings and stay healthy. That's pretty much the main goal."