Blanton (10-13) posted his first victory in a month, limiting the Rockies to seven hits. The right-hander didn't issue a walk and struck out six en route to the crucial win.
Ronald Belisario and Kenley Jansen each shut Colorado down without a run for an inning and Brandon League racked up his sixth save as Los Angeles gained a game on the St. Louis Cardinals in the race for the final National League wild card spot.
The Cardinals lost to Washington Saturday, shaving their lead over the Dodgers to two games with four contests remaining.
Kemp went 3-for-4 with solo shots in the fourth and eighth innings for Los Angeles.
The Rockies' Tyler Chatwood (5-6) lasted four innings, yielding two runs on five hits.