With nearest rivals Besiktas and Galatasaray both dropping points in Round 29 of action, Fenerbahce's victory put them 12 points clear with just five matches remaining.
Caner Erkin handed the high-flying hosts a 21st-minute lead, but they were pegged back by Isaac Promise's strike 10 minutes later.
Michal Kadlec restored their advantage seven minutes before the break, and the Czech added a third with a minute to go.
In the final stages, the visitors saw Serkan Balci sent off for a second caution, before Moussa Sow put the seal on an emphatic victory for the hosts.
Ersun Yanal's men travel to second-placed Besiktas on Sunday knowing that a win will earn them their first top-flight crown since 2011.
Besiktas were held 1-1 at Konyaspor on Friday, with Theofanis Gekas' last-minute equaliser cancelling out Oguzhan Ozyakup's opener.
Galatasaray, meanwhile, fell to only their fourth league defeat of the season, going down 2-1 at Sivasspor.
Aatif Chahechouhe put the hosts ahead in the 17th minute, but Gala were level by half-time thanks to Yekta Kurtulus.
John Utaka's winner on the hour left the visitors a point behind Beskitas in the race for UEFA Champions League football.
Bottom club Kayserispor look in deep trouble after a 2-0 home reverse at the hands of Rizespor left them six points from safety, while Kayseri Erciyesspor picked up what could prove to be a valuable point in a 0-0 draw at Genclerbirligi.
Elazigspor claimed a crucial three points on Monday as goals from Batuhan Karadeniz and Deniz Yilmaz helped them to a 2-1 home win over Gaziantepspor, a result that lifted the hosts out of the bottom three.
In the race for the UEFA Europa League, Trabzonspor will be kicking themselves after surrendering a two-goal lead to draw 2-2 at Eskisehirspor.
Erkan Zengin scored twice from the penalty spot to cancel out first-half efforts from Ozer Hurmaci and Paulo Henrique, while Aykut Demir saw red for the visitors.
They remain in fourth place, above Sivasspor on goal difference, while Karabukspor lie a point further back after a 2-0 home defeat to Akhisar Belediyespor.
Elsewhere, Kasimpasa and Bursaspor finished 1-1.
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