Fenerbahce suffered a crushing 2-1 defeat against Ankaragucu at the Eryaman stadium in the Super Lig on Saturday.
The Yellow Canaries have now dropped points in their last two games resulting in them falling into 6th place on 38 points, six points behind leaders Trabzonspor who have a game in hand.
Lobjanidze opened the scoring for the home side and Rodrigues doubled their lead with a cracking strike on 75 minutes.
Serdar Aziz did manage to pull one goal back in the sixth minute of additional time but it turned out to be nothing more than a consolation goal.
The Yellow-Navies will take on bitter rivals Galatasaray next in the Intercontinental derby.
Ankaragücü: 2 – 1 Fenerbahçe
Stat: Eryaman
Hakemler: Mete Kalkavan, Ceyhun Sesigüzel, Serkan Ok
MKE Ankaragücü: Friedrich, Kitsiou, Kulusic, Alihan Kubalas, Pinto, Lukasik, Sedat Ağaçay (Dk. 61 Atila Turan), Faty, Lobjanidze (Dk. 73 İlhan Parlak), Michalak (Dk. 87 Pazdan), Rodrigues
Fenerbahçe: Altay Bayındır, Isla (Dk. 74 Mevlüt Erdinç), Serdar Aziz, Jailson, Dirar, Luiz Gustavo, Ozan Tufan, Deniz Türüç, Kruse, Tolga Ciğerci (Dk. 46 Emre Belözoğlu-Dk. 66 Ferdi Kadıoğlu), Vedat Muric
Goller: Dk. 13 Lobjanidze, Dk. 75 Rodrigues (MKE Ankaragücü), 90+6 Serdar Aziz (Fenerbahçe)