INTERNATIONAL: Monfils let out a roar as he secured the upset on the sixth match point in front of an adoring California crowd with a backhand winner to set up a meeting with Spanish teenager Carlos Alcaraz in the fourth round.
"I'm quite happy right now - I'm in my zone," Monfils said. "I moved quite good and then I changed the speed quite a lot."
The Frenchman handed Medvedev the break in the ninth game of the first set with a pair of double faults and two forehand errors, as the reigning U.S. Open champion dropped just four points on his serve in the opener.
But Medvedev lost the momentum in the second set, unable to convert on five of six break-point opportunities.
Monfils broke him in the fourth game with a backhand winner and again in the eighth with a fiery forehand.
Overcoming obvious exhaustion, Monfils won the first four games of the final set as Medvedev was unable to set up a single break point opportunity.
It was the first time in 13 years that the 35-year-old Monfils beat the number-one ranked player in the world.
Twenty-times Grand Slam winner Novak Djokovic is expected to return to the top of the world rankings when they are updated.
Nadal sent Evans packing with a routine win to extend his unbeaten streak this year to 17-0 after winning a men's record-breaking 21st Grand Slam title at the Australian Open.
Down an early break, the Spaniard leveled it in the eighth game and again broke Evans to close out the first set and seize the momentum.
He dropped just two first-serve points in the second set, breaking his opponent early and wrapping up his 400th Master’s match win with a forehand winner before thrusting his hands in the air to cheer from the crowd.
He reaches the fourth round after staging a breath-taking, three-set comeback on Saturday against American Sebastian Korda and said after the match he was pleased to wrap up Monday's affair in a tidier fashion.
"Happy to be able to keep going in the tournament," Nadal said. "I think after a few games I have been playing better and better."