Fernandez made a number of spectacular saves against a rampant Bavarian side, led by in-form Frank Ribery, who scored the first goal in the first half.
Lukas Podolski netted Bayern’s second goal almost immediately after the second half began.
The defeat leaves Bielefeld one spot above the relegation zone with two fixtures left to play.
The former Ernst Middendorp-coached side is one point ahead of FC Nurenberg and two in front of Duisburg with Hansa Rostock propping up the table.
Fernandez’s two South African team mates Sibusiso Zuma and Siyabonga Nkosi both made appearances in the match.
Zuma started but was substituted in the 67th minute while Nkosi did not have much chance to impress as he came on as a late substitute 10 minutes later.