Stan Wawrinka pulled out of the Swiss Indoors Basel, where Marin Cilic cruised, while Kevin Anderson won in Vienna.
Despite losing the first set to Stan Wawrinka, Borna Coric took the next two to advance to the last 32 at the Shanghai Masters.
World number four Juan Martin del Potro beat Albert Ramos-Vinolas in straight sets at the China Open.
Martin Klizan inflicted a semj-final defeat on Stan Wawrinka in St. Petersburg and will take on top seed Dominic Thiem in the final.
Dominic Thiem said he was lucky to beat Daniil Medvedev in his homeland to reach the last four in St. Petersburg.
Stan Wawrinka needed to win a pair of tie-breaks to beat Karen Khachanov in their round-of-16 match at the St Petersburg Open.
After a shaky start, Stan Wawrinka came through in straight sets against Aljaz Bedene and will now face Karen Khachanov in St Petersburg.
Rafael Nadal eventually outlasted Karen Khachanov at Flushing Meadows, where the likes of Milos Raonic and Kevin Anderson also won.
Juan Martin del Potro eased through at the US Open as Andy Murray was beaten by Fernando Verdasco.
Back playing a grand slam for the first time in more than a year, Andy Murray came through the US Open first round.