Tomas Soucek proved to be the hero of the afternoon as his close-range finish sent the Irons up to fifth in the Premier League table.
The score line didn't quite reflect the game as a whole as David Moyes' side had many opportunities to make the final result more comfortable than what it was.
In the first half the hosts struck the post twice, while a free-kick from Aaron Cresswell had Jose Sa scrambling across his goal-line.
Chances continued to arrive throughout the opening period, and Declan Rice was the next to go close.
The on-pitch captain was 25 yards out and produced a stunning effort that struck the top right of the post.
Closing in on half-time, the hosts hit the woodwork again when Manuel Lanzini got on the end of a Michail Antonio cross.
Although they were dominated in the first 45 minutes, it could have been Wolves who were going into the break in a winning position.
Hwang Hee-Chan should have done better when sending his shot wide of the post after receiving the ball in a very good position, just inside the West Ham penalty area.
That was as good as it got though for Bruno Lage's men who missed out on their own chance of keeping in touch with the other clubs who currently occupy European spots.
Much of the second half was a replica of the first, but on this occasion, the home crowd had something to cheer about.
After good play on the left from Cresswell and Antonio, the latter sent a low ball across the six-yard box and Soucek was on hand to tap in.
The game should have been put beyond doubt minutes later but Jarrod Bowen placed his effort straight into the hands of Sa, despite having the whole goal to aim for.
Thankfully for David Moyes, the missed opportunity was not capitalised on by Wolves and the Irons keep up their pursuit of a place in the Premier League's top four.