PSV grab last-gasp winner
Tilburg finished with nine men after late second-half red cards for Denis Halilovic and Veli Lampi.
Bart Biemans put Tilburg ahead after 17 minutes but early in the second half Swede Ola Toivonen equalised before Zeefuik clinched the points.
PSV remain top with 47 points after 21 matches, four more than Twente Enschede, who host struggling Feyenoord on Sunday.
Iceland's Kolbeinn Sigthorsson scored five as AZ Alkmaar thrashed lowly VVV Venlo 6-1.
The 20-year-old striker, who joined Alkmaar in July last year, opened the scoring after five minutes when he took advantage of a defensive blunder by Ferry de Regt.
Sigthorsson added two more before Ahmed Musa pulled one back eight minutes before the break and then the Icelander lifted his season total to nine with two more in the second half.
Alkmaar are fifth on 37 points, 10 behind PSV.