Eveland, who has been up with the big club twice before this year and posted a 1-3 record with an 8.00 ERA while making six starts and appearing out of the bullpen once, was 8-6 with a 4.94 ERA and .273 opponents' batting average in 21 starts with the River Cats.
He went 0-4 with a 7.88 ERA over his final five starts for Sacramento, but Eveland, 25, suggested the numbers aren't reflective of how he's felt on the mound.
"I've actually been throwing pretty well," he said, noting that he's added a cut fastball to his arsenal. "The results aren't what I've wanted, but I've had some tough luck. Hopefully I can turn that around up here."
Having moved long reliever Edgar Gonzalez into what's now a six-man rotation, A's manager Bob Geren said Eveland will work out of the bullpen for the time being. If Gonzalez struggles, Eveland might get a start or two.
"He'll probably go into Edgar's slot for now," Geren said of Eveland.
Blevins, who was on Oakland's Opening Day roster, joins the A's for the third time this year, having compiled a 12.46 ERA in five relief appearances over his first two stints. He has a 5-3 record with two saves and a 3.84 ERA in 45 relief appearances with Sacramento, striking out 62 batters in 63 1/3 innings.
"I've been feeling great," said Blevins, who also is throwing a cutter and recently ironed out some mechanical issues that brought his fastball velocity back into the low- to mid-90s neighborhood, in which he lived while posting a 3.11 ERA in 36 appearances with the A's last season.
Kilby, 26, is looking to make his Major League debut after five seasons in the Minors. He was 4-2 with two saves, a 2.13 ERA and .179 opponents' batting average in 45 relief appearances with Sacramento this year, striking out 77 in 63 1/3 innings. A 29th-round pick in the 2005 First-Year Player Draft out of San Jose State University, Kilby, a Northern California (Elk Grove) native, has 339 strikeouts in 295 2/3 career Minor League innings, an average of 10.3 per nine innings.
"He's definitely thrilled to be here," Geren said. "He threw [Monday] night, but I'd like to get him in there as soon as possible."
Geren said the additional relievers won't have much of an impact on the respective workloads of bullpen mainstays such as Craig Breslow, Brad Ziegler, Michael Wuertz and Andrew Bailey, but lesser lights such as Santiago Casilla might get less work from here on out.