Barnsley head coach Valerien Ismael praised his side for battling through to a 2-1 triumph over South Yorkshire rivals Rotherham.
Barnsley scored two well-worked goals in the first 15 minutes to put themselves in a commanding position.
Woodrow then started the second move himself with a pass out to Callum Styles who squared for Mowatt to power in a curling effort from the edge of the box.
It put Barnsley in control but Rotherham fought back in the second half with an effective direct approach.
Barnsley hung on to claim a fourth win from five and further strengthen an unlikely play-off bid.
Ismael said: "You see the quality from Rotherham in the second half. They believe in the principle and that is why it is never an easy game against them.
"The boys did the job perfectly in the first half. The second half was more of a fight.
"I think we played forceful in the first half and we deserved to score two goals and take the lead. In the second half it was a completely different game and we missed the possibility to score the third goal with Victor.
"We have a positive finish for 2020 but we know now that we face a tough January. We have to stay focussed and take games one-by-one."
Rotherham manager Paul Warne praised his depleted squad for putting up a fight after they missed numerous training sessions and had the last two fixtures postponed.
A host of players were missing through injury and positive Covid-19 results meaning he could only name six substitutes.
He said: "I knew going into the game it was going to be a bit agricultural. It wasn't going to be one for the purists.
"The first chance they get, they put away. And they are very good at counter-attack and took their second goal very well.
"We were competing but we didn't have much quality really. We changed it at half time and we created enough in the second half to come away with a point.
"On another day those chances drop in. It wasn't to be.
"As a manager, I am really proud of them. The lads could have crumbled but they were really dogged and could have got a point in the end."