After a woeful display in the opening 45 minutes, Wolves came to life in explosive fashion by scoring twice in 180 seconds at the start of the second half.
Eastwood, whose Carling Cup goal for Southend United last season knocked out Manchester United, broke the deadlock in the 46th minute before Jody Craddock doubled their advantage with a spectacular volley.
It was rough on Bradford who were left to wonder what might have been.
But, to their credit, Bradford refused to wilt and they ensured Wolves endured a nervy final 12 minutes when Kyle Nix scored from six yards.
He pounced in the 77th minute after on-loan Gillingham striker Guylain Ndumbu-Nsungu had seen his shot blocked.
Bradford had been the far more threatening side in the first half, but it was the finishing of the teams that proved to be the deciding factor.
Bradford were unfortunate not to take a lead into half-time and their failure to convert their chances was crucial.
It needed a well-timed challenge from Craddock to block Barry Conlon's goalbound 10th minute drive and, five minutes later, debutant goalkeeper Graham Stack had to dive full length to push away Omar Daley's low drive.
Daley then sliced wide after a surging run into the area as Wolves struggled to get into gear.
They only threatened briefly when Michael Kightly forced a smart near post save from Donovan Ricketts after 28 minutes.
Eastwood and Andy Keogh then conspired to both mis-hit a cross from Jamie Clapham before Wolves were given another major let-off four minutes before half-time.
Stack completely misjudged a right-wing free-kick from Paul Evans and was relieved to see the ball crash to safety off the post.
Wolves took full advantage of that escape and when Keogh helped on a cross from Stephen Ward, Eastwood was on hand to head the ball home from six yards.
Bradford were still reeling from that setback when their fate was sealed three minutes later.
The Bradford defence only half cleared a corner from Kightly and the ball fell invitingly to Craddock whose first-time volley from 20 yards whistled straight past Ricketts.