Last month the Irish sealed qualification for Euro 2016 in France after the Southampton midfielder netted twice in a 3-1 home victory over Greece.
Davis was at it again on Friday, scrambling in the rebound from close range after Latvia keeper Andris Vinans had gone down low to his right to save his header following a pinpoint through ball from Craig Cathcart.
Corry Evans then shot narrowly over from long range as the Irish turned on the style, the home fans showing their appreciation with cries of 'Ole, Ole'.
The 30-year-old Davis, who has now scored eight goals in 79 international appearances, was given a rousing ovation by the crowd when manager Michael O'Neill took him off with seven minutes left.
The Irish had gone 23 matches without a victory in a friendly, stretching back to March 2008.
Latvia offered little threat in attack but were tough to break down at the other end.
The closest they went to a goal was when substitute Artjoms Rudnevs volleyed narrowly wide in the 89th minute.
(Writing by Tony Jimenez; Editing by Greg Stutchbury)
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