Verdasco, the 2009 Australian Open semifinalist, beat sixth seed Roberto Bautista-Agut in an epic three set battle (6-4 3-6 7-5) that lasted two hours and 25 minutes.
Donskoy then went on to win the next two games breaking Federer and he himself had a chance to put the second set to bed, holding a 6-5 lead with his own service game to follow.
The Scot booked his place in the quarter-finals with a crushing 6-2 6-0 win over Guillermo Garcia-Lopez and he will now take on Philipp Kohlschreiber. "I've never even practised with him", the world No. 116 said of what turned out to be a positive for him, his biggest weapon on a night Federer wasn't feeling his best.
With that win against the talented but erratic Spaniard, Murray entered the quarterfinals keeping his hopes of a maiden Dubai title alive.
It's that quality again that came to the fore on a handsome Wednesday evening as Murray beat Garcia-Lopez 6-2 6-0 in 72 minutes at the Dubai Duty Free Tennis Championships.
The mercurial Monfils needed one hour and 35 minutes to beat Evans 6-4 3-6 6-1 in the second match of the day.
Murray, playing in his first tournament since a fourth round defeat at the Australian Open last month, is showing no signs of being match rusty despite having to deal with a case of shingles.
Police raid Francois Fillon's home in fake jobs probe
New opinion polls continued to show Fillon would fail to make the second round of the April/May election, albeit by a narrow margin.
PSA Buys Opel From GM, Will Announce Deal On Monday, Says Report
However, much of the existing Opel lineup would remain dependent for years on technology and parts shared with other GM brands. GM stock was up more than 1 percent Friday afternoon, trading at about $38.18 a share.
McIlroy lurks, Scott struggling in Mexico
McIlroy is keen to continue playing at the WGC-Mexico Championship and was hoping the food poisoning was just a day thing. It's a pleasure to play a golf course where your caddie doesn't hand you the driver walking off the previous green.
Seventh seed Lucas Pouille of France beat Romanian qualifier Marius Copil 6-1 6-4 and will next play Donskoy.
"It was very tough at the start, we both had chances in those early games", Murray, who has never won the Dubai showpiece, said. "So many times I didn't know what his patterns were".
"I loosened up a bit after that and played really well".
Kohlschreiber posted a 6-4 6-4 second-round win over Daniil Medvedev.
"Every time we have played, we have had a lot of close matches", Murray said of Kohlschreiber. He uses the angles of the court well.
The world number 12 moves into a clash with Spain's Fernando Verdasco, who needed nearly two and a half hours to overcome sixth-seeded compatriot Roberto Bautista Agut 6-4, 3-6, 7-5.
Robin Haase upset fifth-seeded Tomas Berdych 3-6, 6-3, 6-4 to set up a quarterfinal meeting against Damir Dzhumur, who defeated Marcel Granollers 6-3, 6-4.