The leaders have 70 points with two matches remaining and can secure the crown next week with a victory at home to bottom club Willem II Tilburg.
Breda, five points above the relegation playoffs, played well in the first half and went close to scoring when a header from Eric Botteghin hit the bar.
Iceland striker Kolbeinn Sigthorsson then put the visitors in front two minutes into the second half when he netted despite having his back to goal.
Five minutes later Tim Gilissen headed the ball into his own goal as he tried to clear a corner at the near post.
"It wasn't easy today. They started at a furious pace and put us under pressure but the opening goal settled us down," said Ajax skipper Siem de Jong.
Jeremain Lens struck twice as second-placed PSV Eindhoven remained four points off the pace with a 5-2 win over Groningen.
Tim Matavz, Dries Mertens (penalty) and Mark van Bommel were also on target for PSV while Michael de Leeuw bagged a double for Groningen.
Second from bottom VVV Venlo raced four points clear of Willem II with a 1-1 draw at ADO Den Haag.
The bottom club go down and the next two teams go through to a relegation playoff.
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