The Rockies needed to win one game in the season-closing series to avoid a 100-loss season and they managed two victories over the Diamondbacks.
Jeff Francis (6-7) allowed a run on five hits over five innings for the victory. Arizona put the tying run on third base in the ninth, but Matt Belisle came on to retire the final batter and claim his third save.
Colorado trailed 2-1 heading into the fourth, but Willin Rosrio drove in the tying run on a fielder's choice grounder. LeMathieu followed with what turned out to be the game-winning hit.
A.J. Pollock homered for the Diamondbacks in the third.
The loss went to Ian Kennedy (15-12), who allowed only two unearned runs on six hits in seven innings.
Arizona finished the year at 81-81. The Diamondbacks and Philadelphia Phillies were the only teams in the majors to wind up with a .500 record.
Notable deaths of 2014 [PHOTOS]