Mark Byrne and Luke Gambin were on target for the Bees, who stayed two points clear of the relegation spots against a Fleetwood side who have only won once in their last eight outings.
Byrne reacted fastest to a loose ball in the area to open the scoring before Gambin made sure of the points after a terrible defensive mix-up.
Davids, who was suspended after he was sent off in the 3-2 defeat at Accrington on Saturday, said: "It's always good to bounce back.
"The players performed really well and I think we really stepped up because we have had a couple of injuries and also a couple of sick players.
"I'm very happy and they showed some real backbone. Three players were sick at home including Jake Hyde, our key striker.
"But we play a certain system so the players who came in knew what they were doing.
"We just have to do our part in the relegation battle and then afterwards we will look at the others but at the end of the day you have to go to the end.
"Even if the other teams do not do well you still have to get the points in. In the last three games luck was not on our side but in that game it was and we really worked for it with the first goal."