Krajinovic is ranked 149 in the world, but the Serb needed only 55 minutes to see off world number 15 and the second seed Fognini 6-4 6-0 in the second round.
Fognini beat Federico Delbonis to win this tournament last year, but he cut a frustrated figure as he went out with a whimper along with another six seeds.
Krajinovic, 22, allowed Fognini only two break points and the outsider took five of the 10 he earned to claim a major scalp on a day for the underdogs.
The Serb set the tone by breaking Fognini, a beaten semi-finalist at the Mercedes Cup last week, in the second game and despite being unable to serve out the set at 5-3 up, he responded by breaking back immediately.
While there was not much to choose between the two players in the first set, Krajinovic was totally dominant in the second, as he lost only eight points to win at a canter.
Krajinovic will now face Dusan Lajovic, who claimed the scalp of Portugal Open winner and 15th seed Carlos Berlocq 6-3 6-4.
It was also a day to remember for wildcard Alexander Zverev, as the teenager beat fifth seed Mikhail Youzhny 7-5 7-5.
Youzhny struggled as he won just 53 per cent of points on serve and 17-year-old German Zverev claimed four breaks to secure a shock straight-sets win.
Zverev, ranked 285th in the world, is the first 17-year-old to beat a top 20 player for a decade - with Richard Gasquet the last man to achieve that feat when he got the better of Nicolas Nassu in the Portugal Open.
Fernando Verdasco was another seed to crash out on Wednesday as Dustin Brown battled back to win 4-6 6-2 7-6 (10-8).
Brown fired down nine aces and saved seven break points as he saw off the ninth seed from Spain to set up a clash with Pablo Andujar, who beat Thomas Bellucci 6-4 3-6 6-2.
Delbonis' hopes of going one better and winning the tournament a year after the 13th seed was a beaten finalist were ended by a 6-3 6-4 defeat to wildcard Tobias Kamke.
Guillermo Garcia-Lopez (10) and Joao Sousa (14) were the other two seeds to bow out in the second round, as they were beaten by Leonardo Mayer and Lukas Rosol respectively.
Fourth-seeded Alexandr Dolgopolov did make progress, beating Jerzy Janowicz 6-4 6-1, while Andreas Seppi and Philipp Kohlschreiber also went through to the third round along with Gilles Simon - who benefited from a walkover when Martin Klizan pulled out due to injury.