Brown knocked in four three-pointers and fellow guard Blake slotted three, the last of them with just 18.8 seconds left on the clock, as the Lakers came from 15 points behind.
The lead changed hands four times in the last minute of a gripping contest at the Staples Center before Blake's final shot sealed the win.
Brown ended up with 16 points and Blake finished with 10.
Guard Kevin Martin top-scored with 26 points while Aaron Brooks contributed 24, including four of six three-pointers, for the Rockets who led throughout the second and third quarters.
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