The Bantams will want to be as strong as possible against a Grecians side who are unbeaten in their last 18 matches, but manager Derek Adams takes heart from the fact his players have produced their best football against League Two's in-form sides.
"We've come off a run of good performances and results against the top teams and we have to do that again because we come up against an Exeter side 18 games unbeaten so they're on an excellent run and they've had a terrific spell," said the Scot.
"We have to break that club record.
"We've done well against the likes of Forest Green, Swindon, Exeter and Port Vale at the top of the table. We can compete against the top teams and we have to go there and score more than them."
Saturday was a case in point, coming from behind to take a point at Port Vale with a Lee Angol header. Vale had scored 17 goals in their previous four matches.
"Port Vale thought that was their toughest test of the season which is a huge compliment to us.
Bradford will be without their seven-goal top-scorer Andy Cook, who has a hamstring injury. The recent returns of Angol and Theo Robinson have helped offset that, but it would be nice to see more of Lavery, who has only made two starts in an injury-hampered Valley Parade career since joining as a free agent in the summer.
"He's the one we're going to try and assess this morning to see if he's going to come with us or not. The only one who's definitely out is Andy Cook."
The winners of Tuesday's replay will go into the second round, and for League Two clubs that means vital revenue. Bradford could certainly do without a long midweek trip and Adams believes they should not need one.
"On the day (of the first game, a 1-1 draw, like all the last four games have been) we probably should have won - we hit the bar, we hit the post and we had a number of really good opportunities," he argued.