Now that he's replicated the feat at a new level, his start back in May now might be just another footnote for the 22-year-old right-hander.
Graham allowed one hit over six innings as the Double-A Mississippi Braves blanked the visiting Huntsville Stars, 2-0, on Tuesday.
Atlanta's No. 7 prospect struck out five batters and walked one in his longest start since his promotion to the Southern League.
"This is up there. It's exciting to get to Double-A and have an outing like this," Graham said. "Now I just want to finish strong. It's my first full season and I've done well at this point starting in High-A and getting called up to Mississippi."
No batter reached second base against Graham, who was selected by the Braves in the fourth round of the 2011 Draft out of Santa Clara University. He threw 58 of 88 pitches for strikes.
After retiring the side in order in the first inning, Graham (2-1) yielded a single to Hunter Morris on a bloop fly ball to left field with one out in the second.
Graham then set down the next 10 batters he faced -- just one ball left the infield -- before Kentrail Davis drew a two-out walk in the fifth. But Graham struck out Adam Weisenburger to preserve the shutout bid, and he worked a 1-2-3 sixth to complete his night.
"I got a lot of ground balls and all of my pitches were working. The defense helped me out, and catcher [Mathew Kennelly] and I were on the same page," said Graham, who relied on a combination of four- and two-seam fastballs, a slider and a changeup.
"The connection was there. He was throwing down pitches and I was thinking the same thing. Once I got into trouble, I started using the fastball more, but I was developing the secondary pitches."
The outing lowered his Southern League ERA to 3.41 and helped him improve to 11-2 across two levels this year.
The California native was 9-1 with a 2.63 ERA in 17 starts with Class A Advanced Lynchburg in the Carolina League before his callup. He struck out four times as many batters as he walked (68 to 17), and he held opponents to a .236 average over 102 2/3 innings.
Among those starts was the gem he fired against Wilmington on May 17. He allowed an unearned run on a lone hit over six innings, but he left in a 1-1 tie and ended up not factoring into the decision after the bullpen allowed a second run in the following frame.
"I believe I have lived up to my own expectations," Graham said. "But there is still work to be done. I get a little amped up some times out there and I start to get wild, so I have to hold that back. There's lots to work on."
On Tuesday, center fielder Todd Cunningham was 3-for-4 with a double and a run scored out of the leadoff spot, and left fielder Evan Gattis added a double and a run-scoring infield single.
Huntsville starter Josh Stinson (11-7) allowed two runs -- one earned -- on eight hits and three walks over six innings. He struck out two hitters and uncorked two wild pitches.