Arkadiusz Milik opened the scoring just two minutes in but the visitors had to wait until the 76th minute for Anwar El Ghazi to double their lead.
PSV, last year's champions, dropped down into second after their first defeat since losing at Wolfsburg in the Champions League in October and their only loss at home all season.
A late equaliser from Stefan Thesker saw FC Twente and AZ Alkmaar draw 2-2 in a match which saw both sides reduced to 10 men at De Grolsch Veste.
Vincent Janssen opened the scoring for visitors AZ with his 21st goal of the season early in the second half.
The hosts lost Zakaria El Azzouzi to a straight red card for elbowing Ridgeciano Haps on the hour mark, minutes before Alkmaar lost Stijn Wuytens to his second yellow of the afternoon.
Thesker brought Twente level with 15 minutes remaining but Thom Haye struck back as the visitors went 2-1 up. Thesker got his second of the afternoon with an impressive header in the last minute of stoppage time.
Vitesse Arnhem moved up to seventh position after an impressive 3-0 win at Groningen. Teenage English striker Dominic Solanke scored twice in the second half, either side of Valeri Qazaishvili's effort, with all three goals coming in a 12-minute spell.
Elsewhere, ADO Den Haag secured a 1-0 win over NEC Nijmegen from their mid-table battle after an 89th-minute goal by Dion Malone.