Kelly gave up three hits and fanning five over six innings, but didn't factor into the decision as Double-A San Antonio blanked Arkansas, 2-0.
MLB.com's preseason No. 22 prospect got stronger as the game went on, retiring eight of the final nine batters to face him. He ended his night by fanning Dillon Baird with catcher Ali Solis throwing out Luis Jimenez trying to steal second base on the play to end the sixth.
Kelly, a former first-round pick by the Red Sox in 2008, threw 91 pitches -- 59 for strikes -- and faced five over the minimum for the Missions.
"I was getting ahead in the count," Kelly said. "That's kind of been my struggle in the last couple of outings. I had my curveball and my change-up working for strikeout pitches tonight."
The 21-year-old Florida native had been pitching well until his last outing, when he surrendered seven runs in five innings against Corpus Christi on May 19. In his four starts prior to that, he was 2-1 with a 2.25 ERA, not allowing more than three runs in a start. Kelly said he didn't change anything heading into Wednesday's game.
"Even though I gave up seven runs, I still had good stuff," the 6-foot-3 right-hander said. "Tonight, I did the same thing I've done all year and tried to compete. I had a good defense behind me and they made some plays to help me out."
Kelly, acquired on Dec. 6 from Boston in the Adrian Gonzalez trade, has pitched significantly better this season, going 4-1 with a 3.83 ERA in 10 Texas League starts. Contrast that to 2010, when he was 3-5 and gave up 118 hits in 95 innings for Double-A Portland.
"I am just trying to get better in every outing," Kelly said. "I think I am a better pitcher than I was last year and a better pitcher than I was in Spring Training."
Being in camp this spring proved to be a valuable learning experience for the former shortstop, who is entering his second full season on the mound.
"Last year was my first full season and I was a thrower rather than a pitcher," Kelly said. "This year I've been working on how to set up hitters, and the biggest thing so far is learning how to pitch and what pitches to throw in what situations.
"In Spring Training, just being around big league pitchers and listening to them talk and absorb everything they talk about was a help," he added.
Jaff Decker singled in a run in the ninth for his 41st RBI of the season, and James Darnell homered and doubled twice for San Antonio.
Craig Italiano was credited with his third win for the Missions, after allowing two hits in two innings of relief. Brad Brach closed out the ninth for his 13th save.
Starter Andrew Taylor gave up three hits over six shutout innings, but didn't factor into the decision for the Travelers.