Israel-born Schlesinger, who won gold at the same venue in May, missed the events in Paris and Dusseldorf because of illness and injury.
But in Baku she went straight to the semi-finals as top seed and outclassed Khanim Huseynova of Azerbaijan.
The 28-year-old then beat Slovenian Andreja Leski in the final.
Schlesinger's superior experience and physicality told and she was able to secure the arm lock and force Leski to tap.
The result also earned the British judoka 1000 world ranking points.
Britain's Alice Schlesinger marked her first competitive outing of 2017 with gold in the -63kg class at the Baku Grand Slam in Azerbaijan.