Fognini is the top seed in Stuttgart and he demonstrated why as Andrey Golubev was beaten 6-4 6-4 by the world number 15.
There were only five break points in the match and it was Fognini who took the opportunities that came his way to set up a last-eight encounter with Santiago Giraldo, who beat Philipp Davydenko, in the ATP 250 clay-court event.
The Italian took the initiative by claiming a break in the third game of the match and Golubev was unable to respond as Fognini took the opening set.
And just the one break was needed in the second set to see out the match, as Fognini marched on in his quest to win a second ATP title of the year.
Second seed Mikhail Youzhny also advanced at the expense of Leonardo Mayer, who struggled with his serve and was made to pay.
Mayer doubled-faulted six times and won only 10 points on his first serve as he was comprehensively beaten 6-1 6-1.
Ruthless Youzhny won the first five games of the match to set the tone and Mayer never recovered from a poor start as he crashed out in an hour and 10 minutes. And his Russian opponent faces another Argentine in the last eight in the form of Federico Delbonis.
Roberto Bautista Agut overcame a second-set blip to beat Louk Sorensen 6-3 1-6 6-1.
The second seed from Spain won the only break point of the first set to take a 5-3 lead and served out the set, but lost his way in a one-sided second set as Sorensen levelled the match.
Bautista Agut responded in the third set, though, and won 82 per cent of points on his first serve as well as breaking twice to progress to the quarter-finals.
Feliciano Lopez also needed three sets to get the better of fellow Spaniard Daniel Gimeno-Traver and the fourth seed had to come from behind to win 6-7 (3-7) 6-2 6-3.
Fifth seed Philipp Kohlschreiber crashed out in his second game of the day as he was beaten 7-5 7-6 (7-5) by Lukas Rosol, having beaten Jan-Lennard Struff earlier in the day in a game that was not completed on Wednesday due to the weather.
Federico Delbonis also advanced on Thursday as he beat Benjamin Becker 6-7 (6-8) 6-4 6-4 and will now face Youzhny, while Guillermo Garcia-Lopez was another winner.