PSV have 37 points from 17 matches, level with Twente Enschede who beat neighbours Heracles Almelo 3-2 on Friday.
Vitesse Arnhem, who entertain RKC Waalwijk on Sunday, are third with 34 points.
Mathias Jorgensen marked his second league appearance for PSV by heading them in front after 10 minutes.
Dick Advocaat's team dominated the rest of the game and went close early in the second half when wingers Luciano Narsingh and Jeremain Lens missed good chances.
Palsson, 21, then made PSV pay for their profligacy in front of goal when his excellent curling shot found the top corner for hosts Nijmegen with 10 minutes to go.
"We were in control but we needed to take our chances to decide the match," said skipper Mark van Bommel.
US international Jozy Altidore struck twice in the first half to halt a streak of six matches without a win for 12th-placed AZ Alkmaar as they triumphed 2-1 at PEC Zwolle.
Zwolle had Joey van den Berg sent off 12 minutes from time for a professional foul.
Elsewhere, Groningen and Roda JC Kerkrade were held 0-0 at home by VVV Venlo and NAC Breda respectively.
- Sports & Recreation
- Twente Enschede
- Heracles Almelo
- Jeremain Lens
- RKC Waalwijk
- Luciano Narsingh