Los Angeles has played 14 games against teams from the NL West this season and has won 11 of them.
The contest was tied at 2-2 through seven innings and both teams scored twice in the eighth -- the Rockies rallying on a two-run homer by Clint Barmes.
Los Angeles then regained the lead in the ninth against Manny Corpas (0-1), who gave up a leadoff double to James Loney and a two-out single to left by Ausmus. That made a winner out of Hong-Chih Kuo (1-0), despite the fact he gave up the homer to Barmes in the eighth.
Broxton came on to start the bottom of the ninth and promptly got in trouble when second baseman Orlando Hudson threw the ball away on a grounder by Garrett Atkinson.
One out later, Troy Tulowitzki drew a walk, putting the tying and winning runs on base. Broxton, however, struck out both Seth Smith and Chris Iannetta to end the game and earn his sixth save. Iannetta fouled off four straight fast balls before swinging and missing.