Let $H$ be a Hilbert space with the norm $|\cdot |$, and let $A:D(A)\subset H\to H$ be a positive self-adjoint unbounded linear operator on H such that $-A$ generates a $C_0$ semi-group on $H$. Let $\phi$ be in $H,$ $E>\epsilon$ a given positive number and let $f:[0,T]\times H\to H$ satisfy the Lipschitz condition $|f(t,w_1)-f(t,w_2)\parallel \le k|w_1-w_2|,$ $w_1,w_2\in H$, for some non-negative constant $k$ independent of $t$, $w_1$ and $w_2$. It is proved that if $u_1$ and $u_2$ are two solutions of the ill-posed semi-linear parabolic equation backward in time $u_t+Au=f(t,u)$, $0<t\le T,$ $|u(T)-\phi |\le \epsilon$ and $|u_i(0)|\le E$, $i=1,2,$ then $$|u_1(t)-u_2(t)|\le 2{\epsilon }^{t/T}{E}^{1-t/T}\exp [(2k+\frac{1}{4}{k}^2(T+t))\frac{t(T-t)}{T}]\mathrm{\forall }t\in [0,T].$$ The ill-posed problem is stabilized by a modification of Tikhonov regularization which yields an error estimate of Hölder type.