It was a positive showing by Market Drayton who looked to have gotten something from the game heading into the last 10 minutes with it all square at 1-1.
The hosts had taken the lead when Rivel Mardenborough netted in the 35th minute meaning they went into the interval with a 1-0 advantage, but the visitors reacted well in the second half, and Reece Taylor made it 1-1 six minutes after the restart.
But their hopes of getting a point were dashed in the 84th minute when Mardenborough got his second of the afternoon as they regained the lead.
And Darlaston hung for all three points.
That result was a blow for Shifnal Town, as it draws the two clubs' level on points as they both target promotion.
Shifnal's game against Racing Club Warwick was postponed due to the weather, so they do have a game in hand on third-placed Darlaston, and league leaders Walsall Wood who they now trail by nine points.
It was not the only game to be called off either as Whitchurch Alport's clash with Lye Town did not go ahead because of the heavy rain.
In Division One, AFC Bridgnorth's hopes of surviving the drop were dealt a blow when they lost a relegation clash to Heath Hayes 2-1 at home.
The visitors went 2-0 up, but Jack Luckett got one back for the Shropshire side and they were unable to find an equaliser that would have given them a valuable point.
Bridgnorth now replaces Heath Hayes in the bottom three.
Shawbury United got the better of Nuneaton Griff in a six-goal thriller.
There were four goals in the first half with it ending 2-2 after an entertaining opening 45 minutes, but Shawbury got the better of them in the second half adding two further goals.
Haughmond remained bottom of the league as their clash against Paget Rangers was called off due to the inclement weather which appeared to hit Shropshire harder than the rest of the Midlands.
And finally, in the North West Counties League Division One South Ellesmere Rangers' game against Stockport Georgians was another game to be impacted by the wet conditions in the county as it was postponed.