Rybakina, Rublev reach Madrid Open last 16
The Kazakh, who has a tour-leading three titles this season after triumphing in Stuttgart last week, broke twice in the first set to move 5-0 ahead on the Spanish clay.
Although Sherif battled harder in the second set, surviving four match points to hold for 5-4 down, Rybakina clinched the victory on serve at the Caja Magica.
"Despite the score, it was a very tough match," said Rybakina, who has the best record on the tour this season with 28 wins.
"It was a lot of deuces and we both fought a lot -- I'm really happy with the performance today."
Rybakina will face teenager Sara Bejlek in the next round after the Czech defeated American Ashlyn Krueger 6-3, 6-1.
"I've never played against a player like this," said the 18-year-old. "I will try my best and we'll see how it will go tomorrow."
In the men's draw Andrey Rublev came back from 5-0 down in a first set tie-break to beat home favourite Alejandro Davidovich Fokina 7-6 (12/10), 6-4 in a nervy affair.
The world number eight kept his nerve and saved five set points to stun his opponent, before a similarly hard-fought second set.
Rublev broke for a 5-4 lead with a shot which the Spaniard chose to leave as he thought it was long, but Hawk-Eye showed it was in by a whisker.
The Russian wrapped up his win with a forehand winner, his second win of the week after four straight defeats.
Last year's Madrid runner-up Jan-Lennard Struff defeated France's Ugo Humbert 7-5, 6-4.
The German could face last year's victor Carlos Alcaraz in the last 16 if the Spaniard defeats Thiago Seyboth Wild later Sunday.