The 46-game streak of reaching base is the longest in the Majors since the Orioles' Kevin Millar reached in 52 straight from June 20-Aug. 25, 2007.
Cuddyer, who went 1-for-4 and has a .344 batting average, admitted having some intrusive streak-related thoughts during the last at-bat.
"It's hard not to," Cuddyer said, laughing. "But at the same time, what kept me from being anxious was the fact we needed baserunners in that situation."
Cuddyer took a slider for a ball and a fastball for a strike, and was able to tap a 2-1 slider that Rosario tipped with his bare hand before the ball rolled past shortstop Brandon Crawford and into center field.
Before Sunday, Cuddyer was 3-for-6 with a double against Giants starter Madison Bumgarner, but was fruitless in three tries against him Sunday.
With runners at first and third and one out in the first, Bumgarner enticed Cuddyer to whiff on a 2-2 curveball low and out of the strike zone.
"Obviously, it [the streak] is in your head, but there's a job at hand," Cuddyer said. "I was upset with myself that first at-bat because the job was to get that guy in from third with less than two outs, and I didn't. That was bigger than the streak to me, and I didn't come through."
Cuddyer grounded to short to open the fourth inning, and grounded to third in the sixth.
Cuddyer's streak is the longest in the Majors since the Red Sox's David Ortiz hit in 27 games, but across two seasons -- July 2, 2012-May 7, 2013. The last longer same-season streak was fashioned by the Braves' Dan Uggla, who recorded a hit in 33 straight games in 2011 from July 5-Aug. 13.
Cuddyer has hit safely in 53 of his 59 starts.
"It's been fun watching him do this," Rockies manager Walt Weiss said. "It's nice to see him get some recognition. He's a great player."