Durant poured in 41 points to extend his streak of scoring 30 points or more to 11 games as the Thunder erased a 14-point deficit for the win.
Paul Millsap scored 23 points for the Hawks, including a game-tying lay-up with 22 seconds to play, but Durant sealed the victory with just 1.5 seconds on the clock.
Kyle Lowry scored 31 points to lead the Toronto Raptors to a dramatic 104-103 win over the Brooklyn Nets.
Lowry led the offence but it was Patrick Patterson who sealed the win as he stole a misplaced pass from Deron Williams and sunk the winning basket with six seconds left, ending the Nets' five-game winning streak.
Kevin Love scored 31 points as the Minnesota Timberwolves beat the Chicago Bulls for their first win in eight.
Elsewhere the Los Angeles Clippers beat the Milwaukee Bucks 114-86, the Phoenix Suns were 124-113 winners over the Philadelphia 76ers and the Utah Jazz saw off the Sacramento Kings 106-99.