The Brit heard a bawl as he was taking part in a volley within the third space - which got here from Fognini - and knowledgeable him to "shut up" as they argued at the changeover, with Murray sad that the umpire had no longer intervened.
Twice he served for the match, but a faltering first serve gave Fognini an opportunity that he did not turn down and he ran away with the tie-break against a visibly tiring Murray.
Meanwhile, Swiss second seed Roger Federer eased past Spain's Albert Ramos-Vinolas in his opening match.
"These last few weeks I have played more matches", Murray said. "To play him again in the same circumstances basically I knew could be unsafe, and that's why I'm very pleased how I was able to control the match".
Medvedev could meet Djokovic in the semi-finals of Shanghai, which would be their first meeting since the world number one lost to him in Cincinnati in August. [Fognini] then told me "stop looking at me, what are you looking at me for".
Man Utd eyeing cut-price Christian Eriksen transfer as Tottenham stance revealed
It's down to us players to take responsibility", Kane told Sky Sports ahead of Spurs' league clash with Southampton on Saturday. They will be without Giovani Lo Celso and Ryan Sessegnon, due to respective hip and hamstring problems.
With the win, Fognini will go on to play unseeded American Taylor Fritz or seventh seeded Russian Karen Khachanov.
I'm practising as hard as I can and playing my best in the tournaments also."By reaching five consecutive finals (Washington, Montreal, Cincinnati, US Open, St. Petersburg), Medvedev joined the last four players to finish No. 1 in the ATP Rankings going back to 2004, who all have reached five or more consecutive finals in their careers".
The 21-year-old was forced to save three consecutive set points at 3/6 in the first-set tie-break and nearly let a 5-1 lead slip in the second set, before converting his sixth match point. His past two matches with Djokovic both took place this season, and Djokovic sealed two victories. But I think with experience I know that they'd rather see me win the match, not play as pretty and as spectacular, but see me in the next round rather than me trying to hit the insane shots all the time and trying to please them.
Serbia's 16-time Grand Slam champion, who won the Japan Open last week without dropping a set, cruised to a 6-3 6-3 second-round victory.
"From the beginning I was sharp, I brought the right intensity and focus on the court", said the Serbian.
He will next play Frenchman Lucas Pouille who eliminated Chinese wildcard Li Zhe 6-7 (4-7), 6-4, 6-4.