Moore bagged his sixth goal in the last six games and Woodrow made it five from five as Barnsley beat Southend United 4-2, with Mike Bahre adding a late fourth.
The Tykes had a scare when Southend had a goal disallowed – which would have made it 3-3 – but Daniel Stendel’s side were worthy winners.
“We had so many chances to score and we were the better team,” said Stendel. “It was not easy but it was a real victory for us in the end and we deserved it.
“We definitely had more chances than them so it was a shock Southend seemed to have scored a third but the better team was us.”
Barnsley broke the deadlock in the 41st minute when Moore headed home Alex Mowatt’s right-wing corner from close range.
Southend equalised in stoppage time when Sam Mantom’s corner from the left was deflected into his own net by Moore.
But Barnsley regained the lead when Shrimpers goalkeeper Mark Oxley fumbled a corner from Mowatt and Woodrow was on hand to net the rebound.
The Tykes then made it 3-1 when Bahre’s cross from the right was tapped in by Woodrow.
Southend got back into the game in the 84th minute when Timothee Dieng headed home. Shrimpers then saw Michael Turner’s volley ruled out for offside, before Barnsley wrapped up the win in stoppage-time as Bahre fired home.
Southend United: Oxley, Bwomono, White, Turner, Hendrie, McLaughlin, Mantom, Yearwood (McCoulsky 76), Kightly (Bunn 76), Dieng, Cox (Robinson 76). Unused substitutes: Hyam, Bishop, Moore, Hutchinson.
Barnsley: Davies, Brown, Pinnock, Lindsay, Fryers (Pinillos 68), Bahre, McGeehan, Mowatt, Moncur, Moore (Potts 81), Woodrow (Adeboyejo 90). Unused substitutes: Cavare, Jackson, Thiam, Greatorex.
Referee: P Marsden (Lancashire).