Goals either side of half-time from Kevin McDonald and Nouha Dicko earned Wanderers a fourth successive win to keep their bid to make an instant return to the Championship on track.
McDonald's second goal in two games in first-half injury-time and a second strike in three matches for Dicko after 57 minutes following his £300,000 move from Wigan sealed the points against a Bradford side who had to play for more than an hour with 10 men after the dismissal of Nathan Doyle.
Jackett said: "It is tight between the top three in truth and it is all now about going forward.
"I am pleased to be in the race for promotion and I am really looking to push on now and earn that automatic place.
"The three clubs, and probably Preston as well, will think they have got a chance.
"We have now got to look to keep working hard on the training ground and to improve the pattern of play which is quite constructive and very much possession-based.
"I was delighted with the win and it makes it very tight at the top which is great and we are looking, in the last 17 games of the season, to be as fit and as strong as we possibly can.
"I felt that our football was good again. We didn't perhaps do enough with it and up and around the box we were a little bit slow with our play and slow with our passing and didn't take the chance to maybe have a strike and have a strike at the edge of the box.
"But we got two goals, we can't complain, and a very good clean sheet but we were somewhat wasteful in possession I thought up and around their box.
"Bradford are a very spirited team and well organised. They have a good manager and were unlucky not to score themselves after hitting the woodwork twice."
Jackett admitted that the dismissal of Doyle was a major turning point.
He added: "Any team going down to 10 men is a big moment in the game and I felt that then we tried to make the pitch as big as we possibly can.
"We were playing quite well before that without scoring goals and to get that first goal just before half-time I felt was a crucial one. It gave us a big lift going into the break.
"To win four games is great and I am very pleased to be as consistent as that. It was a great clean sheet as well. That is key as well, defensively, where we are not giving much away."