Edinburgh's victory, a week after they lost 16-6 to Glasgow at Scotstoun, saw them bolster their chances of a top-six finish as they climbed to joint seventh in the standings.
Victory was secured courtesy of a brace of first-half tries from Tim Visser, the second one being an interception score which began in the winger's own 22.
Sam Hidalgo-Clyne, who had already kicked two penalties, converted both and Edinburgh led 20-3 at half-time.
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A try two minutes after the restart by scrum-half Nikola Matawalu, added to Finn Russell's first-half penalty, should have given Glasgow something to build on but with their pack being outplayed there was no way back.
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