Managed by former England coach Steve McClaren, Twente will secure the crown if they beat NAC Breda away in their final game of the season on May 2.
Twente have 83 points from 33 matches, one ahead of Ajax Amsterdam who kept up their relentless pressure on the leaders with a 4-0 drubbing of Heracles Almelo. Ajax play away at NEC Nijmegen in their final game.
"We have put ourselves in a great position after a difficult match and are now just one win away from our target," McClaren, who joined Twente in July 2008 after failing to guide England to Euro 2008, told reporters.
Twente, who suffered their second league defeat this season in losing to AZ Alkmaar in midweek, made a nervous start against cup finalists Feyenoord and wasted several good chances before opening the scoring five minutes before the break.
Bryan Ruiz set up Swiss international Blaise Nkufo to break the deadlock and midway through the second half Miroslav Stoch broke through the Rotterdam side's defence to secure the points.
"We made a nervous start today but it was good to see how my team handled this week's defeat against AZ," added McClaren.
"We knew the opening goal would be crucial and from that point we were in control."
Siem de Jong struck twice before the break to put Ajax in control against Heracles and Marko Pantelic added a double in the second half to lift Ajax's goal tally to 102.
PSV Eindhoven came from behind to beat Groningen 3-1 to remain third on 77 points.
Tim Matavz put Groningen ahead after three minutes but youngster Zakaria Labyad's double and a goal from Balazs Dzsudzsak turned the tide for PSV.
At the other end of the table ADO Den Haag beat already relegated RKC Waalwijk 4-0 to stay in the top flight.
Sparta Rotterdam and Willem II Tilburg are condemned to play in the relegation play-offs.
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