diff --git a/src/solutions/ode_solutions.jl b/src/solutions/ode_solutions.jl
index c9c023863..589331a53 100644
--- a/src/solutions/ode_solutions.jl
+++ b/src/solutions/ode_solutions.jl
@@ -189,7 +189,9 @@ function (sol::AbstractODESolution)(t::Number, ::Type{deriv}, idxs,
         continuity) where {deriv}
     symbolic_type(idxs) == NotSymbolic() && error("Incorrect specification of `idxs`")
     if is_parameter(sol, idxs)
-        return getp(sol, idxs)(sol)
+        unknown_tidx = searchsortedfirst(sol.t, t; lt = <=) - 1
+        ps = parameter_values_at_state_time(sol, unknown_tidx)
+        return getp(sol, idxs)(ps)
     else
         return augment(sol.interp([t], nothing, deriv, sol.prob.p, continuity), sol)[idxs][1]
     end
@@ -200,14 +202,19 @@ function (sol::AbstractODESolution)(t::Number, ::Type{deriv}, idxs::AbstractVect
     all(!isequal(NotSymbolic()), symbolic_type.(idxs)) ||
         error("Incorrect specification of `idxs`")
     interp_sol = augment(sol.interp([t], nothing, deriv, sol.prob.p, continuity), sol)
-    [is_parameter(sol, idx) ? getp(sol, idx)(sol) : first(interp_sol[idx]) for idx in idxs]
+    unknown_tidx = searchsortedfirst(sol.t, t; lt = <=) - 1
+    ps = parameter_values_at_state_time(sol, unknown_tidx)
+    [is_parameter(sol, idx) ? getp(sol, idx)(ps) : first(interp_sol[idx]) for idx in idxs]
 end
 
 function (sol::AbstractODESolution)(t::AbstractVector{<:Number}, ::Type{deriv}, idxs,
         continuity) where {deriv}
     symbolic_type(idxs) == NotSymbolic() && error("Incorrect specification of `idxs`")
     if is_parameter(sol, idxs)
-        return getp(sol, idxs)(sol)
+        unknown_tidxs = searchsortedfirst((sol.t,), t; lt = <=) - 1
+        pss = parameter_values_at_state_time.((sol,), unknown_tidxs)
+        getter = getp(sol, idxs)
+        return getter.(pss)
     else
         interp_sol = augment(sol.interp(t, nothing, deriv, sol.prob.p, continuity), sol)
         p = hasproperty(sol.prob, :p) ? sol.prob.p : nothing
@@ -222,7 +229,7 @@ function (sol::AbstractODESolution)(t::AbstractVector{<:Number}, ::Type{deriv},
     interp_sol = augment(sol.interp(t, nothing, deriv, sol.prob.p, continuity), sol)
     p = hasproperty(sol.prob, :p) ? sol.prob.p : nothing
     return DiffEqArray(
-        [[interp_sol[idx][i] for idx in idxs] for i in 1:length(t)], t, p, sol)
+        [[is_parameter(sol, idx) ? getp(sol, idx)(interp_sol, i) : interp_sol[idx][i] for idx in idxs] for i in 1:length(t)], t, p, sol)
 end
 
 function build_solution(prob::Union{AbstractODEProblem, AbstractDDEProblem},