Lee Tomlin made an impact on his first competitive appearance for Boro since his move from Peterborough on deadline day, playing 82 minutes before being replaced by Bryn Morris.
Boggy conditions in the West Midlands - the game was played at Albion's training HQ near Walsall - made it difficult for constructive football to be played throughout the game, but there were flashes.
Connor Ripley, who enjoyed a fine match in his last game away to Manchester United U21s, was called on to make a double save from Alex Jones and Kemar Roofe.
He had earlier saved from Roofe and later denied Alex Jones, while his opposite number Jack Rose twice denied Cameron Park who went close with decent efforts.
The second half started brightly with both sides having a go with Roofe twice going close, hitting the bar with one effort before Boro scored the only goal of the game.
With 54 minutes played Cameron Park ran unchecked from just inside the Baggies half and found the right-hand bottom corner of the net with a well-struck shot from 20 yards.
Park had a good chance to score again a few minutes later, but didn't make good contact when attempting to head a Ryan Brobbel's left-wing cross.
It took a terrific save from Rose 16 minutes from time to prevent Brobbel scoring from close range, but Albion thought they had found a way through five minutes from time.
Liam O'Neil tucked in after a free-kick was flicked on, but he was in an offside position and the goal was not allowed to stand.
"The lads showed a great attitude after the Stoke defeat," said a delighted coach Graeme Lee.
"It was a solid defensive performance and good to keep a clean sheet against a good West Brom side."
West Brom: Rose; W Atkinson, D Daniels, C Jones, Francis, S Nabi (Ward 75), O'Neil, Birch, Roofe (Ward 77), O'Sullivan, A Jones (Wright 75). Unused subs: Palmer (gk); Howkins.
Boro: Ripley; Halliday, Weledji, D Atkinson, Meling, Park, Kitching, Bennett, Brobbel, Tomlin (Morris 82), Kneeshaw (J Jones 70). Unused subs: Coddington (gk), Burn, Fewster.
Referee: M Amphlett