On as a substitute, Crouch netted the 52nd headed goal of his Premier League career from a Xherdan Shaqiri corner on 73 minutes.
Not long after injured referee Bobby Madley was replaced by Jonathan Moss, Vicente Iborra volleyed Leicester ahead from Harry Maguire's knockdown.
Xherdan Shaqiri lifted in Stoke's leveller when Eric Maxim Choupo-Moting played him in six minutes before half-time.
Riyad Mahrez put Leicester 2-1 up after good work from Wilfred Ndidi on the hour mark, before Crouch ended Claude Puel's winning start as Leicester manager.
Stoke: 20 Nov v Brighton (A)
Leicester: 18 Nov v Man City (H)