The home side had goalkeeper Lee Camp to thank for keeping the score down when he kept out a point-blank header with an excellent save on 10 minutes.
Lee Frecklington perhaps should have done better when he met a cross with a header that flew over the crossbar after the home side.
Frecklington went close just before the half-hour mark with a well-struck attempt that whistled just wide.
Wolves restored their advantage at the end of the half when Danny Batth rose highest to power a downwards header home.
After the break, the Millers perhaps should have restored parity when Toffolo's cut-back found Grant Ward, but he could only fire wide from around six yards out.
Wolves came close to extending their lead when Graham's cross found Ethan Ebanks-Landell, but the defender's volley dropped just wide.