A first-half goal from Tubbs was enough to take Crawley to the top of League Two ahead of the afternoon's fixtures but Northampton more than played their part in an entertaining game.
Gary Johnson's side created chances of their own in front of 4,803 at Sixfields but came up just short as they looked to build on successive league wins.
"Our flair players just didn't turn up today which was disappointing," Johnson told the official club website after the game.
"We wanted to put on a performance but unfortunately it just wasn't there for us today."