The German fourth seed will next play 11th seed Kyle Edmund.
Basilashvili's victory over an under-the-weather Del Potro at the weekend was just his second ATP title, the first coming in Hamburg in July.
"I was happy to get out in two", Federer said.
In the second set, both players looked comfortable on serve throughout the set, but when Federer was serving to stay in the set at 4-5, Medvedev played a very strong return game and with a little help from the Swiss at 30-30, he took his only chance to level the match. "I've always played him when he's playing well, but I'll hope I can take it to him".
"That's one of the - probably the - biggest goal of the end of the season". "It's a pity in the sense I played a handsome match, but didn't get a victory. I played every single point as if there was no tomorrow". It's a pity that I lost the opportunity to play with Federer, to see what's the difference between us.
Del Potro, who was hindered by the flu in losing Sunday's China Open final to unseeded Nikoloz Basilashvili, said in Beijing last week that he was running on empty.
Remains of 11 babies found in ceiling of closed funeral home
For those that weren't, like the numerous cremated they are trying to take from here or that they are taking from here. Detroit police will search the entire building to make sure no additional bodies are hidden inside, according to WDIV .
Meghan Markle’s ex-husband marries fiancee in intimate ceremony
At the time, it was reported that the film producer took their split pretty hard, so it's great to see that he's happy again now. Meghan, now The Duchess of Sussex , was married to Trevor for two years in 2011 , after spending nearly 10 years together.
Salah scores Olimpico for Egypt
Salah's goal was his 13th in African Cup of Nations qualifying, overtaking the previous Egyptian record by Hossam Hassan. Group leaders Tunisia, also on six points, host Niger on Saturday.
Razer Phone 2 leaks thanks to premature Amazon listing
Razer will unveil the device at 6:30 PM PT or 7:00 AM IST and the company is set to stream the event live on the Razer website . Predictably, Razer sells a separate wireless-charging dock with the company's iconic Chroma lighting effects for your bedside.
James Murdoch tipped to lead Tesla board
Musk will remain as CEO. "The proposed settlements in this case are fair", lawyers for the SEC, Tesla and Musk said in the filing. The carmaker is considering raising some of the $5 billion it intends to invest in the plant near Shanghai from local partners.
Jadon Sancho surprised by first England call-up
If you're ready to play overseas and you believe in yourself, why not? "I believe in myself in one versus one situations". In response, Sancho failed to turn up for training, eventually sealing his move to the Bundesliga weeks later.
Facebook introduced its own gadget for a smart home
And it also comes bundled with Amazon's voice interface " Alexa ", enabling users to shop or control household appliances. More recently, Facebook revealed that hackers managed to pierce its security to break into 50 million accounts.