The victory took manager Phillip Cocu's side to 80 points from 31 games, an unassailable 10-point lead over second-placed Ajax with three rounds of the season remaining. It was their third championship in four seasons.
Pereiro fired PSV ahead midway through the first half after he reacted quickest when Hirving Lozano's shot was blocked on the line.
The pace of the game was relentless but home nerves were settled when De Jong headed home a second goal from Joshua Brenet's cross.
The title was made safe nine minutes into the second period as Bergwijn showed neat control to bring down a high ball and fired low into the corner of the net.
Ajax had Argentine defender Nicolas Tagliafico sent off for a second bookable offence late on and minutes later they lost Siem de Jong to a straight red card as the visitors were left to contemplate a fourth season in a row without league success.
PSV have led the league since mid-September, suffering just three defeats all campaign, and are second only to Ajax (33) for the most Dutch title wins.
(Reporting By Nick Said; Editing by Toby Davis and Clare Fallon)
