Fresh from their goals against Leyton Orient in the league last weekend, striking duo Billy Clarke and Jon Stead fired the Bantams into a two-goal half time lead over Dartford during the club's second round encounter.
Wingers Filipe Morais, who was recalled after a recent minor shoulder problem, and Mark Yeates, who had earlier set up Stead's goal, then wrapped up the tie for City with a strike each within less than a minute of each other just before the hour mark.
On top of the goals Clarke and Stead scored against Dartford - both of which were the pair's fourth of the season for City - the forward partnership also picked up an assist each during the tie.
Parkinson said: "Jon (Stead) and Billy (Clarke) are both scoring and working hard for the team.
"They are playing well together in attack for us and their all-round game at present is very good.
"The link up play between themselves and our midfielders today (Sunday) was good quality. The lads around them know that they can play the ball into their feet and things will happen for us.
"I am pleased to see Filipe (Morais) on the score-sheet as well.
"He has worked so hard over the last couple of weeks or so to come back from the shoulder injury he picked up against Gillingham and today was his reward. His goal was a great finish.
"He really wanted to be back for this game, and I feel his partnership with Stephen Darby down our right hand side can be a good one for us.
"(Mark) Yeatesy showed some real quality at times during the game and really deserved his goal as well.
"When he gets in and around the box and he has a player one-on-one, you feel something is going to happen. It was an excellent finish by him.
"He scored a tremendous goal at Preston a couple of weeks ago and he has backed it up again today. That is three goals for the season so far for him and he has to keep building on that."