The British number one's reward is a meeting with American world number 22 Steve Johnson - a 6-1 6-1 winner over Russia's Evgeny Donskoy - in the quarter-finals as the Scotsman remains on course to emulate his gold medal success at London in 2012.
But he will have to play better than this to be sure of back-to-back gold medals after looking helpless as world number 40 Fognini won eight straight games and broke for a 3-0 lead in the final set before the world number two Murray restored some sense of normality to the occasion by producing some fine tennis as his opponent wilted despite the support of a noisy posse of Italian fans.
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It was a 15th straight win in singles for Murray since losing to Novak Djokovic in the French Open final in June, but he never expected this one to get tense after blitzing Fognini in the first set with his movement and pace of shot giving the contest a feel of a training contest until his opponent found his range.
Andy Murray in action in Rio.
Image credit: Eurosport
Murray remained in good spirits after the match as he returned to the main court seconds later to sign autographs for fans, no doubt relieved that his participation in the men's singles remains active after being tested by Fognini on a sluggish court that suited the San Remo native's baseline instincts.
It looked like Fognini might repeat his famous straight-sets victory over Murray in the Davis Cup on the clay of Naples two years ago, but Murray found a way to detonate what threatened to torpedo his standing as tournament favourite ahead of Rafael Nadal, who had few similar problems in downing Gilles Simon 7-6 (7-5) 6-3 to secure a quarter-final meeting with Brazil's Thomaz Bellucci.
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