Surrendering four Diamondbacks runs, two on a Tony Clark home run, in the first inning after the Rockies had scored two didn't help.
Kim suffered a thumb contusion while batting in the second and said he couldn't feel or control the ball. After Clark homered again to open the fourth, Kim threw one more pitch and signaled to the dugout that he was done. So were the Rockies, who fell, 6-4, at Chase Field before 21,904.
"I didn't feel real good," Kim said.
Manager Clint Hurdle said Kim displayed "lack of command, and left-handers took good swings. He wasn't able to get he ball to spots he needed to."
So went the opportunity for Kim (1-2), who didn't make the starting rotation this spring and has been hoping for another opportunity, with the Rockies or elsewhere.
Even with the difficult starting effort, the Rockies made it yet another close game. Todd Helton went 2-for-4 with a home run, his first since last Sept. 10, and two RBIs, and finished the series 6-for-13 (.462) with six RBIs.
The Rockies took other forward steps offensively.
Garrett Atkins went 2-for-5 with a first-inning RBI double, and Matt Holliday was 1-for-2 with three walks. They were a combined 9-for-19 in the series.
The Rockies also received lifts from the bench Sunday.
Jamey Carroll, playing second because spark-plug Kazuo Matsui went on the disabled list Sunday with back spasms, went 2-for-5 with a double. Yorvit Torrealba, who is in for more playing time as the Rockies try to help rookie catcher Chris Iannetta through early struggles, was 2-for-4 to lift his average to .300.
Still, the Rockies haven't clicked completely enough this season. They're 5-7, with no loss by more than three runs. They won the first game of series against the Padres, Dodgers and D-backs, but dropped he next two each time and return from their first 2007 road trip 3-6.
However, the Rockies have seven home games within the National League West, starting Monday against the Giants, to begin to click.
"There's always room for improvement," Helton said. "We'll get better. We haven't hit our peak yet, or whatever you want to call it."
But Helton said being close in so many losses is "no consolation -- we're at the point where we should be wining games."
Part of the problem Sunday was batting order misfortune. The Rockies left 11 runners on base, but Kim twice and reliever Taylor Buchholz once came up with runners in scoring position. On two of those occasions, the pitcher was the third out.
To make matters worse, Kim suffered his injury while fouling off a pitch before striking out with Troy Tulowitzki at third base in the second inning. Against left-handed hitters such as Clark, Kim brushed them back but his attempts at inside strikes were hit hard.
"I don't want to use our bullpen," Kim said, explaining why he kept pitching even though he was in pain and ineffective. "The third inning, I was just lucky."
The Rockies scored four runs on nine hits in five innings against winning pitcher Davis (1-1), but managed just one hit against four D-backs relievers. Jose Valverde walked Helton and Holliday with two down in the ninth, but struck out Jeff Baker looking to complete his sixth save.
Thomas Harding is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.