We employ very high resolution simulations of isolated Milky Way-like galaxies to study the effect of triaxial dark matter haloes on exponential stellar discs. Non-adiabatic halo shape changes can trigger two-armed grand-design spiral structures which extend all the way to the edge of the disc. Their pattern speed coincides with the inner Lindblad resonance indicating that they are kinematic density waves which can persist up to several Gyr. In dynamically cold discs, grand-design spirals are swing amplified and after a few Gyr can lead to the formation of (multi-armed) transient recurrent spirals. Stellar discs misaligned to the principal planes of the host triaxial halo develop characteristic integral shaped warps, but otherwise exhibit very similar spiral structures as aligned discs. For the grand-design spirals in our simulations, their strength dependence with radius is determined by the torque on the disc, suggesting that by studying grand-design spirals without bars it may be possible to set constraints on the tidal field and host dark matter halo shape.