Westbrook scored 29 points and Durant went 14-of-16 from the free-throw line en route to 26 for the second-seeded Thunder, who put the defending NBA champions in a big hole in their Western Conference quarterfinal series.
James Harden contributed 15 points, seven rebounds and five assists off the bench for the victors.
Oklahoma City held on for the triumph when Dallas' Jason Terry missed two potential score-tying 3-pointers in the closing seconds.
Toddler uninjured after being knocked over by Obama family dog
Ron Burgundy interviews Peyton Manning on SportsCenter