Promoted from Triple-A Colorado Springs before the game for his second stint with the Rockies this season, Chatwood (2-0) had a shaky second inning but settled in after that and handcuffed the Giants, who managed one run and six hits in 5 2-3 innings.
Rosario made a nifty defensive play to thwart a big second inning and drove in three runs for the Rockies, who beat the Giants for the second straight time after snapping a 10-game losing streak to them with a 10-9 win one night earlier, ending their longest streak over a division opponent since divisional play began in 1969, according to STATS.
Lincecum (3-3) committed a costly throwing error that led to a three-run third inning and also had a balk when he slipped off the mound that led to another run in the fourth before Rosario took him deep for his ninth homer in the fifth.
The Giants' defensive slump continued despite a team meeting before the game in which manager Bruce Bochy addressed San Francisco's poor defense of late.
"You're going to have ups and downs, whether it's hitting or sometimes defensively, but 13 errors in 10 games is too many," Bochy said after the meeting.
Then, he watched the Giants commit three more errors.
Catcher Buster Posey airmailed a throw into center field on Carlos Gonzalez's stolen base attempt in the first inning. Gonzales trotted to third but he was stranded there when Lincecum got Troy Tulowitzki to ground out to short to end the inning.
In the top of the second inning, Posey tried to advance to third on a pitch that got past Rockies catcher Rosario, but the ball ricocheted right back to Rosario, who spun and nailed Posey by several feet. Brandon Belt followed with a two-out double to the right-field corner.
Gregor Blanco drove in Belt with a bloop single to center, and Brandon Crawford drew an intentional walk before Lincecum was caught looking at the third strike, thwarting what could have been a bigger inning.
The Giants' second error proved more costly as Lincecum's bad throw on a comebacker led to a big third inning for Colorado.
Dexter Fowler doubled down the left-field line, scoring Charlie Blackmon from second to tie it at 1. Fowler scored when Lincecum fielded Josh Rutledge's chopper and threw the ball into right field. Rutledge ended up at third base and trotted home on Gonzalez's groundout.
Lincecum slipped off the rubber while pitching to Blackmon in the fourth, resulting in a balk that sent Nolan Arenado to second base. He took third when Blackmon flied out to center and scored on Chatwood's single back up the middle, making it 4-1.
The Giants put runners at the corners in the fifth but Posey grounded out to the mound to end the threat, and Rosario's two-run homer, his ninth, made it 6-1 in the fifth.
All of the six runs Lincecum allowed in five innings were earned. He gave up seven hits and walked a pair.
Rosario's 60-foot dribbler down the third-base line off Jean Machi in the seventh drove in Fowler from third to make it 7-1.
Shortstop Brandon Crawford's RBI single made it 7-2 in the eighth, but he committed San Francisco's third error in the bottom half of the inning when he took his eye off a throw back into the infield, allowing Fowler to advance to second following an RBI single.
Tulowitzki added a two-run single off George Kontos to make it 10-2.
Josh Outman threw two effective innings of relief and Wilton Lopez got the final four outs.
Notes: This is Chatwood's second stint with the Rockies this season. He went 1-0 with a 3.00 ERA in two starts earlier this season before returning to Triple-A. ... Rockies OF Michael Cuddyer says he doubts his neck will bother him again this season after getting an epidural that relieved pain and stiffness. He returned to throwing and taking batting practice Saturday. ... The Giants and Rockies wrap up their four-game series Sunday with LHP Barry Zito (3-2) and RHP Juan Nicasio (3-1) squaring off.