Keys, who was the US Open runner-up a year ago, crashed out 7-5 5-7 6-4 to the Russian on a baking hot Court Three.
Women's top seed and French Open champion Simona Halep, a semi-finalist in 2014 and a quarter-finalist in the last two years, takes on China's 126-ranked Saisai Zheng.
The 38-year-old American - last year's runner-up at Wimbledon - was the oldest entrant in the women's singles field.
German fourth seed Alexander Zverev made the third round, seeing off Taylor Fritz of the United States 6-4, 5-7, 6-7 (0/7), 6-1, 6-2 and faces Latvian qualifier Ernests Gulbis for a spot in the last 16.
Nadal won only 64 per cent of points on his first serve and faced 13 break points - including three in the first game of the match - but he saved 11 of them and converted five of his own to wrap up the win in under 2 1/2 hours on Centre Court.
Federer, making his 20th consecutive appearance at the grass-court Grand Slam, is yet to face a break point from his opening three matches and will now continue his campaign against 22nd-seed Adrian Mannarino.
The Jim Jordan Matter
Jordan's spokesman said the Republican congressman is now working with investigators to set up a meeting. DiSabato told Fox News that Jordan's response to his claims has been "disappointing". "It's not true.
The match on Monday will also be a tussle between two of the tour's mothers. But he easily held serve in the next game and broke Zeballos again to close out the match.
"I tried to hit the ball hard and fight for every ball and I think in the end that's why I won". "I felt my mind go and move on".
The 29-year-old Russian needed treatment after securing the decisive break in the final set, but she was able to block out the pain to seal her upset.
Zverev beat Taylor Fritz of the USA 6-4, 5-7, 6-7 (0), 6-1, 6-2 in a match that was suspended on Thursday after the third set. The second set went back and forth, with both players getting advantages before finally it went to a tiebreak.
It is the biggest win of Pella's career and he is now in the third round of a Grand Slam for the first time.