We study D-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss–Bonnet term and the cosmological term Λ. We find a class of solutions with exponential time dependence of two scale factors, governed by two Hubble-like parameters H> 0 and h, corresponding to factor spaces of dimensions m> 2 and l> 2 , respectively. These solutions contain a fine-tuned Λ = Λ (x, m, l, α) , which depends upon the ratio h/ H= x, dimensions of factor spaces m and l, and the ratio α= α2/ α1 of two constants (α2 and α1) of the model. The master equation Λ (x, m, l, α) = Λ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. The explicit solution for m= l is presented in “Appendix”. Imposing certain restrictions on x, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. We also consider a subclass of solutions with small enough variation of the effective gravitational constant G and show the stability of all solutions from this subclass. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.