The result for PSV means that they will have to wait a little longer until they can confirm their title win.
After a relatively quiet start, it was the hosts that had most of the chances, all coming from some neat wing-play but none of the resulting headers managed to test Jasper Cillessen in the Ajax net.
As the game looked like it would be heading into half time scoreless, Van Rhijn's long-range free kick troubled Bram Castro. The keeper could only palm it straight into the path of Sigthorsson, who duly dispatched the chance to give Ajax a 1-0 lead.
The second half emulated the first, with neither team really able to test the opposition's keeper until Ajax doubled their lead deep into the half.
Lucas Andersen scored four minutes from time and wrapped up the victory for Ajax, making title rivals PSV wait another week until they can claim the Eredivise title.