diff --git a/stdlib/LinearAlgebra/src/bidiag.jl b/stdlib/LinearAlgebra/src/bidiag.jl
index 89bf143b3a973..d412c21f55a94 100644
--- a/stdlib/LinearAlgebra/src/bidiag.jl
+++ b/stdlib/LinearAlgebra/src/bidiag.jl
@@ -502,8 +502,9 @@ end
 
 const SpecialMatrix = Union{Bidiagonal,SymTridiagonal,Tridiagonal}
 # to avoid ambiguity warning, but shouldn't be necessary
-*(A::AbstractTriangular, B::SpecialMatrix) = Array(A) * Array(B)
+#*(A::AbstractTriangular, B::SpecialMatrix) = Array(A) * Array(B)
 *(A::SpecialMatrix, B::SpecialMatrix) = Array(A) * Array(B)
+*(A::AbstractMatrix, B::SpecialMatrix) = A_mul_B_td!(zeros(eltype(A),size(A)...), A, B)
 
 #Generic multiplication
 *(A::Bidiagonal{T}, B::AbstractVector{T}) where {T} = *(Array(A), B)
diff --git a/stdlib/LinearAlgebra/test/bidiag.jl b/stdlib/LinearAlgebra/test/bidiag.jl
index f90a13caddaa3..eff5192ff368e 100644
--- a/stdlib/LinearAlgebra/test/bidiag.jl
+++ b/stdlib/LinearAlgebra/test/bidiag.jl
@@ -290,6 +290,11 @@ srand(1)
     @test Matrix{Complex{Float64}}(BD) == BD
 end
 
+# Issue 27176
+Diag = Tridiagonal([1,],[2,2],[1,])
+Dense = [0.42 0.18; 0.08 0.58]
+@test typeof(Diag*Dense) == typeof(Dense*Diag) == typeof(Dense)
+
 # Issue 10742 and similar
 let A = Bidiagonal([1,2,3], [0,0], :U)
     @test istril(A)