Atlanta (5-3-2) has won four in a row - all by shutout - and five of its last six.
Héctor Villalba, on the left side of the area, dropped it to Martínez, the 2018 South American Footballer of the Year, who side-netted a first-timer in the 14th minute.
Atlanta had 61.7% possession.
Orlando City (3-5-3) is winless in its last three games and has lost three of its last five.
Atlanta's Jeff Larentowicz came on the 76th minute to become the third field player in MLS history with 400 career appearances.
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