diff --git a/lib/OrdinaryDiffEqCore/src/integrators/integrator_interface.jl b/lib/OrdinaryDiffEqCore/src/integrators/integrator_interface.jl
index 306333435b..b1a014ef71 100644
--- a/lib/OrdinaryDiffEqCore/src/integrators/integrator_interface.jl
+++ b/lib/OrdinaryDiffEqCore/src/integrators/integrator_interface.jl
@@ -321,6 +321,8 @@ function terminate!(integrator::ODEIntegrator, retcode = ReturnCode.Terminated)
     integrator.opts.tstops.valtree = typeof(integrator.opts.tstops.valtree)()
 end
 
+const EMPTY_ARRAY_OF_PAIRS = Pair[]
+
 DiffEqBase.has_reinit(integrator::ODEIntegrator) = true
 function DiffEqBase.reinit!(integrator::ODEIntegrator, u0 = integrator.sol.prob.u0;
         t0 = integrator.sol.prob.tspan[1],
@@ -335,6 +337,23 @@ function DiffEqBase.reinit!(integrator::ODEIntegrator, u0 = integrator.sol.prob.
         reinit_callbacks = true, initialize_save = true,
         reinit_cache = true,
         reinit_retcode = true)
+    if reinit_dae && SciMLBase.has_initializeprob(integrator.sol.prob.f)
+        # This is `remake` infrastructure. `reinit!` is somewhat like `remake` for
+        # integrators, so we reuse some of the same pieces. If we pass `integrator.p`
+        # for `p`, it means we don't want to change it. If we pass `missing`, this
+        # function may (correctly) assume `newp` aliases `prob.p` and copy it, which we
+        # want to avoid. So we pass an empty array of pairs to make it think this is
+        # a symbolic `remake` and it can modify `newp` inplace. The array of pairs is a
+        # const global to avoid allocating every time this function is called.
+        u0, newp = SciMLBase.late_binding_update_u0_p(integrator.sol.prob, u0,
+            EMPTY_ARRAY_OF_PAIRS, t0, u0, integrator.p)
+        if newp !== integrator.p
+            integrator.p = newp
+            sol = integrator.sol
+            @reset sol.prob.p = newp
+            integrator.sol = sol
+        end
+    end
     if isinplace(integrator.sol.prob)
         recursivecopy!(integrator.u, u0)
         recursivecopy!(integrator.uprev, integrator.u)
diff --git a/test/interface/dae_initialize_integration.jl b/test/interface/dae_initialize_integration.jl
index 85a119d859..4b223703e6 100644
--- a/test/interface/dae_initialize_integration.jl
+++ b/test/interface/dae_initialize_integration.jl
@@ -76,3 +76,20 @@ sol = solve(prob, Rodas5P(), dt = 1e-10)
 @test sol[1] == [1.0]
 @test sol[2] ≈ [0.9999999998]
 @test sol[end] ≈ [-1.0]
+
+@testset "`reinit!` updates initial parameters" begin
+    # https://github.com/SciML/ModelingToolkit.jl/issues/3451
+    # https://github.com/SciML/ModelingToolkit.jl/issues/3504
+    @variables x(t) y(t)
+    @parameters c1 c2
+    @mtkbuild sys = ODESystem([D(x) ~ -c1 * x + c2 * y, D(y) ~ c1 * x - c2 * y], t)
+    prob = ODEProblem(sys, [1.0, 2.0], (0.0, 1.0), [c1 => 1.0, c2 => 2.0])
+    @test prob.ps[Initial(x)] ≈ 1.0
+    @test prob.ps[Initial(y)] ≈ 2.0
+    integ = init(prob, Tsit5())
+    @test integ.ps[Initial(x)] ≈ 1.0
+    @test integ.ps[Initial(y)] ≈ 2.0
+    reinit!(integ, [2.0, 3.0])
+    @test integ.ps[Initial(x)] ≈ 2.0
+    @test integ.ps[Initial(y)] ≈ 3.0
+end