Rotherham hadn’t wanted the match to go ahead following a glut of injuries and coronavirus cases, but they were able to scramble together a six-man bench with just three players missing out with Covid-19.
But Rotherham showed admirable spirit and launched a comeback after the break, with Michael Smith coming off the bench to set up a nervy final half-four.
Barnsley held on, however, to climb to the lofty heights of eighth in the Championship table, while their neighbours sunk into the relegation zone.
Story of the match
Despite having the first early chance, when Kyle Vassell forced a strong low save from goalkeeper Jack Walton, Rotherham’s lack of preparation was soon exposed by the ruthless Reds.
Both teams looked to play forward quickly but one side was understandably far sharper, and Mowatt’s excellent defence-splitting pass allowed Woodrow to calmly slot in his eighth goal of the season.
The skipper then turned scorer to put Barnsley in true command. The ball was swept from right to left, with Callum Styles allowed to find Mowatt as he in turn curled an exquisite first-time finish across Viktor Johansson from the edge of the box.
Rotherham ceded nothing in fight or quality to their opponents, just lacking focus at the back and harmony in attack. They did still fashion chances, with Freddie Ladapo forcing a Walton save on the turn, but Barnsley held off pressure to see the break.
Paul Warne’s side were always in the first half without making an impression, but in the second half they came to life and launched an admirable comeback.
Smith was introduced at the break and, after firing a warning shot at Walton, cut the deficit before the hour by rising above a crowd of bodies in the six-yard box to head in a Dan Barlaser corner.
The momentum firmly shifting in their favour, Ladapo was presented with a glorious opportunity to equalise moments after the restart when Callum Brittain missed a cross, but the striker fired a whisker beyond the far post.
Ben Wiles also went close to a leveller with a curling effort, after Rotherham received a fortunate let off when Barnsley winger Victor Adeboyejo held off Wes Harding determinedly only to then shoot badly wide.
The chances dried up in the closing stages with only Matt Olosunde testing Walton further, while Styles and Woodrow couldn't take late chances to make the points safe.
Man of the match: Alex Mowatt (Barnsley)
The Barnsley captain covered every blade of grass in a dynamic performance which featured a lovely assist and yet another cracking goal.