The Giants put Marco Scutaro and Pablo Sandoval aboard with two outs in the first and Pence followed by smashing the first pitch from Jorge De La Rosa deep into the left-field seats for a quick 3-0 lead.
Madison Bumgarner (2-0) overcame five walks to earn the victory, yielding a pair of runs on five hits over 5 2/3 innings. The left-hander struck out five.
Sergio Romo struck out the side in the ninth to pick up his fourth save in the opener of a three-game series.
De La Rosa (0-1) ended up allowing just the three runs on six hits over six innings for the Rockies, who came into the game with a 5-1 record.
Carlos Gonzalez pounded a solo homer for Colorado.
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