Milwaukee's O.J. Mayo sent the game into an extra period by hitting a 3-pointer with 11 seconds to go in regulation but the Bucks couldn't sustain that momentum and lost their 10th in a row.
It is Milwaukee's longest losing streak in 17 years.
Gortat scored consecutive baskets in overtime to give Washington a three-point lead and the Wizards went on to win their third straight.
Mayo led the Bucks with 21 points and Khris Middleton had 13.
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