Lurgan batted first and skipper Stevie Chambers was in fine form, scoring 50 not out as the visitors lost just three wickets in setting the home side a target of 133 to win.
Derek Heasley hit 25 and Niranjan Godbole 23.
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Rain then caused a delay at the end of the Lurgan innings and Cliftonville were eventually set a target of 71 to win in nine overs.
They fell eight runs short however, hitting 63 for the loss of five wickets with Niranjan Godbole taking 3 for 15 runs to leave the town side still undefeated at the top of the table.