Garland, who recently signed with the Rockies after being released by Seattle, allowed one run on five hits in six innings.
Carlos Gonzalez drove in Colorado's next two runs with RBI singles in the fifth and seventh innings.
Harang, out of the Dodgers' starting rotation and the subject of trade speculation, said his first-inning problems were partially caused by new glasses that made him dizzy. He went 5 1/3 innings and allowed only one run after Cuddyer's blast.
Kevin Gregg, fighting to make the Dodgers bullpen as a non-roster invitee, lowered his ERA to 0.93 with two-thirds of an inning. Left-hander Paco Rodriguez, however, was charged with a pair of runs in the seventh inning.
Backup catcher Tim Federowicz added some late fireworks for the Dodgers, belting a three-run homer against right-hander Manny Corpas in the eighth inning.
Up next: After a bout with back spasms gave the Rockies a scare, Opening Day starter Jhoulys Chacin will be back on the mound Wednesday, making the 2:05 p.m. MT start against the A's at Phoenix Municipal Stadium. Among the regulars likely to play are Troy Tulowitzki and Todd Helton, who both had Tuesday night's game off.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.