The second seeded Indian took just 40 minutes to tame 13th seed Diehl 21-14, 21-18 in the third round of the women's singles event.
But minutes before the start of Saina's match, world number one and top seed Yihan Wang of China was stunned by Japan's Eriko Hirose in a three-game thriller that lasted an hour fifteen minutes.
Hirose won 20-22 21-16 21-18.
However, Saina did not show any nerves nor did she carry forward the sluggishness that marked her match against Chinese Taipei's Chen in the second round.
The Indian was aggressive from the start and knowing that her opponent Diehl liked long rallies kept the pace slow and killed the game in mid court.
Within minutes of the start Saina was off to a 10-5 lead as Diehl made errors at the net.
Saina's main weapon, the drop shot, was again used to good effect as thrice in a row the Russian could not pick up the shuttle as it dropped inches off the net on her side.
At 18-14, Nehwal reeled off three points in a row, forcing an error at the net from Diehl to win the opening game 21-14.
In the second game, Saina again started off winning five consecutive points on her serve before Diehl won her opening point on a net error by the Indian.
Both the players were a little more wary as the Russian tried to force the pace with a combination of drop shots and high tosses. At 6-6, it seemed that the game would be tough and hard fought, but changed her strategy and played mid court more often and avoided net play till she had a lead of 15-10.
When it almost seemed that the game would go in Saina's favour, the Russian made a last ditch effort and equalised with some smart net play at 17-17.
But Saina's got her composure back to take the lead at 20-18 and finally pocketed the match when Diehl sent the shuttle across the side line.
"I wouldn't say that the first game was easy. I felt better than my second round game and I did control the play. I know she would have liked to play long rallies because that's her strength and I didn't allow that," Saina said after the match.
"I think I am more comfortable with the conditions now. But it's going to get tougher now as higher seeded players will come through but I am prepared," she said.
"It's not that I haven't played quarter-finals before but a World Championship has its own pressures and I think I am used to it," the Indian added.
Saina will next play either 11th seed Jie Yao of the Netherlands or China's sixth seed Shixian Wang on Friday.
In head-to-head clashes, the Dutch player has won twice and Saina once out of three meetings while the Indian is yet to play Wang in any championships.