The Chairboys took control against their League Two opponents with two first-half goals.
But the home side came on strong after the break to make Matt Bloomfield’s side work hard for their win.
Wycombe had gone in front on 19 minutes as David Wheeler nodded down Ryan Tafazolli’s deep cross for Killian Phillips to run onto and smash past Harry Lewis from 12 yards.
Wycombe doubled the lead in the 35th minute. Freddie Potts won the ball back from Emmanuel Osadebe near the Bradford penalty area and home defender Sam Stubbs headed the cross into his own net.
Managerless Bradford were much more of an attacking threat in the second half.
Max Stryjek tipped away Jamie Walker’s shot and then produced a superb reflex save to keep out a header from Andy Cook.
But Walker pulled one back on 64 minutes to set up a tense finish as Bradford pressed hard for an equaliser.