Wood were frustrated when their planned league fixture at Wolverhampton Casuals was called off due to the rain, but Town had no such problems, beating Studley 2-0 with one goal in each half from Kieron Miller and a penalty from Lewis Gill.
It means Town are three points behind Wood in second place, having played one game more.
manager Dean Gill said: "Our team are very comfortable in their game at the minute on and off the pitch and we’re still trying to improve every week, which is testament to everyone’s appetite and we remain humble to collecting as many points as possible.
"We again had three very important players missing against Studley in Liam Smith, Ryan Winwood and Aaron Bishop, but I was able to field the same side for the first time in a long while, which I believed helped us although it will be good to have those lads back in a few weeks time."
Lye Town slipped up in front of 153 spectators at Walshes Meadow as they went down 3-1 at Stourport Swifts. Stourport took the lead on 12 minutes on a difficult pitch but Lye equalised through Josh Hesson nine minutes later. But two second half goals for the home side won it for them, although the game was marred by Swifts' captain Martin Slevin breaking his leg.
The result leaves Lye in fifth place, five points off Wood but having played two games more. Lye are at home to Lichfield City tonight (Tuesday) at the Sports Ground.
Tividale got a welcome win over City on Saturday, 2-0. Arman Khoshkhoo got the opener in the first half and a late Harry Lewis penalty made it 2-0 for Tividale who travel to Highgate United tonight.
In Division One, Dudley Town opened up a 16-point-gap at the top of the table after a thrilling 6-3 win over Bridgnorth Town at the Guardian Warehousing Arena. Daniel Danks and Samuel Yankson both got two goals, with Owen Massey and Alex Perry also on target for the Robins. Luke Morris got two for Bridgnorth including a penalty and Matt Dean their other goal.
Town have played three more games than second placed Ashby Ivanhoe whilst Bridgnorth are now third from bottom after Cradley Town overtook them with a 1-0 win over Coventry Copsewood. Brad Ward got Cradley's goal but they saw substitute Chris Bladen sent off.
OJM Black Country kept up the pressure at the top of the table with a 3-1 win over Ingles. Rabab Ali gave them a two-goal first half lead, with Adam Callinswood adding the third after the break.
OJM travel to Stourport Swifts in the league cup competition tomorrow night (Wednesday).
Mid table Wednesfield got a 1-1 draw at Nuneaton Griff, with Samuel Paddock on target for them. Wednesfield travel to Wolverhampton Casuals in the JW Hunt Cup tomorrow night.
Wolverhampton Sporting Community got a valuable point in a 2-2 draw at Paget Rangers to stay just above Wednesfield – Community are at home to sixth placed Droitwich Spa in the league tonight.