The Orioles also surrendered five walks and hit two batters.
"Quite frankly, looking at the walks and the hit by pitch and the 19 hits, we're fortunate they didn't score more than 11 runs," manager Buck Showalter said.
Eveland, making only his second start of the season and his first since May 11, allowed five runs on six hits and two walks in 3 2/3 innings.
In the past five games, Orioles starters have pitched to an 11.86 ERA, allowing 41 hits in 22 innings.
Since making his only other start, Eveland had been strong in a long-relief role, pitching to a 2.57 ERA in 21 innings over 10 appearances.
But, after getting pounded on Saturday, Eveland's ERA is up to 4.11.
"Nothing went right," Eveland said. "Never really found my sinker today, which is a pitch I know I have to have."
Hunter, who was in the mix to start Saturday, came on in relief of Eveland and surrendered five runs on eight hits in 1 2/3 innings.
"I left the ball up and they took advantage of it," Hunter said. "It is what it is. You can't make excuses. Get the ball down and the results will come."
Hunter, among the Major League leaders in home runs per nine innings, allowed another long ball to Shelley Duncan in the sixth inning Saturday.
Hunter is 3-4 with a 6.11 ERA following his most recent outing.
"I'm not throwing the way I should or the way I can," Hunter said. "I've got to figure something out."
The majority of the Orioles offense came from Chris Davis, who blasted a three-run home run onto Eutaw Street in the fourth inning to draw the O's within 5-4.
But they never got any closer.
Even as Luis Ayala, Kevin Gregg and Matt Lindstrom combined to allow only one run over the final 3 2/3 innings, the damage surrendered by Hunter and Eveland proved too much to overcome.
"I struggled, and because I did that, I wore out the bullpen, which I hate doing," Eveland said. "Being down there, I know what it's like having to throw and use that many guys. And I know what happens the rest of the week, us not having any off-days the rest of the week, nobody's going to get any rest. Unfortunately, I messed that up a little bit."
With the Orioles needing fresh arms in the midst of a stretch of 13 games in 13 days, one or both of Hunter and Eveland could be headed back to Triple-A Norfolk.
"I've done it before," Hunter said. "I've just got to figure it out, and let them take care of whatever they've got to do."
"I just want to be part of this group," Eveland said. "I feel like we got something special."
Miguel Gonzalez, who was scheduled to start for Norfolk on Saturday, was scratched prior to the game. Gonzalez has a 2.45 ERA in two long-relief appearances with the O's this season.
"Obvioulsy we'll need some length tomorrow," Showalter said. "We'll see what we're going to do."